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Commit b1737687 authored by Alexandre Duret-Lutz's avatar Alexandre Duret-Lutz
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translate: add a quick syntactic simplification before relabeling 

This fixes #412.

* spot/twaalgos/translate.cc: Add the quick syntactic simplification.
* spot/twaalgos/relabel.cc: Do not register old unused APs.
* tests/core/ltl2tgba2.test: Add test case.
* tests/core/bdd.test, tests/python/automata.ipynb: Adjust.
* NEWS: Mention this.
parent 1c5468a9
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NEWS
View file @ b1737687
......@@ -45,6 +45,9 @@ New in spot 2.9.3.dev (not yet released)
file. With this refactoring, we can retrieve both a kripke or a
kripkecube from a PINS file.
- Translations for formulas such as FGp1 & FGp2 &...& FGp32 which
used to take ages are now instantaneous. (See issue #412.)
Bugs fixed:
- Handle xor and <-> in a more natural way when translating
......
spot/twaalgos/relabel.cc
View file @ b1737687
......@@ -32,6 +32,7 @@ namespace spot
std::set<int> newvars;
vars.reserve(relmap->size());
bool bool_subst = false;
auto aplist = aut->ap();
for (auto& p: *relmap)
{
......@@ -42,6 +43,10 @@ namespace spot
throw std::runtime_error
("relabel_here: new labels should be Boolean formulas");
// Don't attempt to rename APs that are not used.
if (std::find(aplist.begin(), aplist.end(), p.first) == aplist.end())
continue;
int oldv = aut->register_ap(p.first);
vars.emplace_back(oldv);
if (p.second.is(op::ap))
......
spot/twaalgos/translate.cc
View file @ b1737687
......@@ -418,7 +418,7 @@ namespace spot
if (simpl_owned_)
{
// Modify the options according to set_pref() and set_type().
// We do it for all translation, but really only the first one
// We do it for all translations, but really only the first one
// matters.
auto& opt = simpl_owned_->options();
if (comp_susp_ > 0 || (ltl_split_ && type_ == Generic))
......@@ -436,33 +436,61 @@ namespace spot
// sub-formulas that are Boolean but do not have common terms.
//
// This rewriting is enabled only if the formula
// 1) has some Boolean subformula
// 2) has more than relabel_bool_ atomic propositions (the default
// 1) has more than relabel_bool_ atomic propositions (the default
// is 4, but this can be changed)
// 2) has some Boolean subformula
// 3) relabel_bse() actually reduces the number of atomic
// propositions.
relabeling_map m;
formula to_work_on = *f;
if (relabel_bool_ > 0)
{
bool has_boolean_sub = false; // that is not atomic
std::set<formula> aps;
to_work_on.traverse([&](const formula& f)
{
if (f.is(op::ap))
aps.insert(f);
else if (f.is_boolean())
has_boolean_sub = true;
return false;
});
atomic_prop_collect(to_work_on, &aps);
unsigned atomic_props = aps.size();
if (has_boolean_sub && (atomic_props >= (unsigned) relabel_bool_))
if (atomic_props >= (unsigned) relabel_bool_)
{
formula relabeled = relabel_bse(to_work_on, Pnn, &m);
if (m.size() < atomic_props)
to_work_on = relabeled;
else
m.clear();
// Make a very quick simplification path before for
// Boolean subformulas, only only syntactic rules. This
// is to help getting formulas of the form
// FGp1 & FGp2 & ... & FGp32
// into the shape
// FG(p1 & p2 & ... & p32)
// where relabeling will be much more efficient.
//
// We reuse all options of simpl_ (to preserve things
// like keep_top_xor or favor_event_univ).
tl_simplifier_options options = simpl_->options();
options.synt_impl = false;
options.containment_checks = false;
options.containment_checks_stronger = false;
options.nenoform_stop_on_boolean = true;
options.boolean_to_isop = false;
tl_simplifier simpl(options, simpl_->get_dict());
to_work_on = simpl.simplify(to_work_on);
// Do we have Boolean subformulas that are not atomic
// propositions?
bool has_boolean_sub = false;
to_work_on.traverse([&](const formula& f)
{
if (f.is_boolean())
{
has_boolean_sub = true;
return true;
}
return false;
});
if (has_boolean_sub)
{
formula relabeled = relabel_bse(to_work_on, Pnn, &m);
if (m.size() < atomic_props)
to_work_on = relabeled;
else
m.clear();
}
}
}
......
tests/core/bdd.test
View file @ b1737687
#!/bin/sh
# -*- coding: utf-8 -*-
# Copyright (C) 2017, 2018 Laboratoire de Recherche et Développement de
# Copyright (C) 2017, 2018, 2020 Laboratoire de Recherche et Développement de
# l'Epita (LRDE).
#
# This file is part of Spot, a model checking library.
......@@ -30,7 +30,7 @@ grep 'spot: BDD package initialized' err
# This value below, which is the number of time we need to garbage
# collect might change if we improve the tool or change the way BuDDy
# is initialized.
test 63 = `grep -c 'spot: BDD GC' err`
test 11 = `grep -c 'spot: BDD GC' err`
# Minimal size for this automaton.
# See also https://www.lrde.epita.fr/dload/spot/mochart10-fixes.pdf
test "147,207" = `autfilt --stats=%s,%e out`
tests/core/ltl2tgba2.test
View file @ b1737687
......@@ -27,7 +27,7 @@
# commonly use as benchmark change, we want to notice it.
set -e
genltl --dac --eh --sb --hkrss --p --format=%F,%L,%f >pos
genltl --dac --eh --sb --hkrss --p --and-fg=32 --format=%F,%L,%f >pos
(cat pos; ltlfilt --negate pos/3 --format='!%<,%f') |
ltlfilt -u -F-/3 >formulas
......@@ -201,6 +201,7 @@ p-patterns,16, 2,16, 2,16, 2,16, 2,16
p-patterns,17, 3,20, 3,20, 3,20, 3,20
p-patterns,18, 5,36, 5,36, 5,36, 5,36
p-patterns,20, 1,8, 1,8, 3,24, 3,24
and-fg,32, 2,4294967298, 2,4294967298, 2,4294967298, 2,4294967298
!dac-patterns,1, 2,4, 2,4, 2,4, 2,4
!dac-patterns,2, 3,10, 3,10, 3,10, 3,10
!dac-patterns,3, 3,12, 3,12, 3,12, 3,12
......@@ -357,6 +358,7 @@ p-patterns,20, 1,8, 1,8, 3,24, 3,24
!p-patterns,17, 4,31, 4,31, 4,31, 4,31
!p-patterns,18, 6,43, 6,43, 6,43, 6,43
!p-patterns,20, 3,16, 3,16, 3,16, 3,16
!and-fg,32, 1,4294967296, 1,4294967296, 2,8589934592, 2,8589934592
EOF
diff output expected
......
tests/python/automata.ipynb
View file @ b1737687
%% Cell type:code id: tags:
``` python
from IPython.display import display
import spot
from spot.jupyter import display_inline
spot.setup()
```
%% Cell type:markdown id: tags:
To build an automaton from an LTL formula, simply call `translate()` with a formula, and a list of options to characterize the automaton you want (those options have the same name as the long options name of the `ltl2tgba` tool, and they can be abbreviated).
%% Cell type:code id: tags:
``` python
a = spot.translate('(a U b) & GFc & GFd', 'BA', 'complete'); a
```
%%%% Output: execute_result
![](data:image/svg+xml;utf8,<?xml version="1.0" encoding="UTF-8" standalone="no"?><!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN""http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd"><!-- Generated by graphviz version 2.43.0 (0)--><!-- Pages: 1 --><svg width="460pt" height="329pt"viewBox="0.00 0.00 460.00 328.80" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g id="graph0" class="graph" transform="scale(1.0 1.0) rotate(0) translate(4 324.8)"><polygon fill="white" stroke="transparent" points="-4,4 -4,-324.8 456,-324.8 456,4 -4,4"/><text text-anchor="start" x="204.5" y="-290.6" font-family="Lato" font-size="14.00">[Büchi]</text><!-- I --><!-- 0 --><g id="node2" class="node"><title>0</title><ellipse fill="#ffffaa" stroke="black" cx="56" cy="-120" rx="18" ry="18"/><text text-anchor="middle" x="56" y="-116.3" font-family="Lato" font-size="14.00">0</text></g><!-- I&#45;&gt;0 --><g id="edge1" class="edge"><title>I&#45;&gt;0</title><path fill="none" stroke="black" d="M1.15,-120C2.79,-120 17.15,-120 30.63,-120"/><polygon fill="black" stroke="black" points="37.94,-120 30.94,-123.15 34.44,-120 30.94,-120 30.94,-120 30.94,-120 34.44,-120 30.94,-116.85 37.94,-120 37.94,-120"/></g><!-- 0&#45;&gt;0 --><g id="edge2" class="edge"><title>0&#45;&gt;0</title><path fill="none" stroke="black" d="M49.62,-137.04C48.32,-146.86 50.45,-156 56,-156 60.17,-156 62.4,-150.86 62.71,-144.14"/><polygon fill="black" stroke="black" points="62.38,-137.04 65.85,-143.88 62.54,-140.53 62.71,-144.03 62.71,-144.03 62.71,-144.03 62.54,-140.53 59.56,-144.18 62.38,-137.04 62.38,-137.04"/><text text-anchor="start" x="38" y="-159.8" font-family="Lato" font-size="14.00">a &amp; 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<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7f9f5d7cbd50> >
<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7f37382c04b0> >
%% Cell type:markdown id: tags:
The call the `spot.setup()` in the first cells has installed a default style for the graphviz output. If you want to change this style temporarily, you can call the `show(style)` method explicitely. For instance here is a vertical layout with the default font of GraphViz.
%% Cell type:code id: tags:
``` python
a.show("v")
```
%%%% Output: execute_result
![](data:image/svg+xml;utf8,<?xml version="1.0" encoding="UTF-8" standalone="no"?><!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN""http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd"><!-- Generated by graphviz version 2.43.0 (0)--><!-- Pages: 1 --><svg width="343pt" height="360pt"viewBox="0.00 0.00 343.40 360.00" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g id="graph0" class="graph" transform="scale(0.9259259259259258 0.9259259259259258) rotate(0) translate(4 386)"><polygon fill="white" stroke="transparent" points="-4,4 -4,-386 368.02,-386 368.02,4 -4,4"/><text text-anchor="middle" x="182.01" y="-350.8" font-family="Times,serif" font-size="14.00">[Büchi]</text><!-- I --><!-- 0 --><g id="node2" class="node"><title>0</title><ellipse fill="none" stroke="black" cx="235.02" cy="-287" rx="18" ry="18"/><text text-anchor="middle" x="235.02" y="-283.3" font-family="Times,serif" font-size="14.00">0</text></g><!-- I&#45;&gt;0 --><g id="edge1" class="edge"><title>I&#45;&gt;0</title><path fill="none" stroke="black" d="M235.02,-341.85C235.02,-340.21 235.02,-325.85 235.02,-312.37"/><polygon fill="black" stroke="black" points="235.02,-305.06 238.17,-312.06 235.02,-308.56 235.02,-312.06 235.02,-312.06 235.02,-312.06 235.02,-308.56 231.87,-312.06 235.02,-305.06 235.02,-305.06"/></g><!-- 0&#45;&gt;0 --><g id="edge2" class="edge"><title>0&#45;&gt;0</title><path fill="none" stroke="black" d="M252.06,-293.38C261.88,-294.68 271.02,-292.55 271.02,-287 271.02,-282.83 265.88,-280.6 259.16,-280.29"/><polygon fill="black" stroke="black" points="252.06,-280.62 258.9,-277.15 255.55,-280.46 259.05,-280.29 259.05,-280.29 259.05,-280.29 255.55,-280.46 259.2,-283.44 252.06,-280.62 252.06,-280.62"/><text text-anchor="middle" x="294.02" y="-283.3" font-family="Times,serif" font-size="14.00">a &amp; 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<spot.jupyter.SVG object>
%% Cell type:markdown id: tags:
If you want to add some style options to the existing one, pass a dot to the `show()` function in addition to your own style options:
%% Cell type:code id: tags:
``` python
a.show(".st")
```
%%%% Output: execute_result
![](data:image/svg+xml;utf8,<?xml version="1.0" encoding="UTF-8" standalone="no"?><!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN""http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd"><!-- Generated by graphviz version 2.43.0 (0)--><!-- Pages: 1 --><svg width="415pt" height="360pt"viewBox="0.00 0.00 414.84 360.00" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g id="graph0" class="graph" transform="scale(0.8849557522123894 0.8849557522123894) rotate(0) translate(4 403)"><polygon fill="white" stroke="transparent" points="-4,4 -4,-403 465,-403 465,4 -4,4"/><text text-anchor="start" x="210" y="-384.8" font-family="Lato" font-size="14.00">Inf(</text><text text-anchor="start" x="231" y="-384.8" font-family="Lato" font-size="14.00" fill="#1f78b4">⓿</text><text text-anchor="start" x="247" y="-384.8" font-family="Lato" font-size="14.00">)</text><text text-anchor="start" x="209" y="-370.8" font-family="Lato" font-size="14.00">[Büchi]</text><g id="clust1" class="cluster"><title>cluster_0</title><polygon fill="none" stroke="green" points="159.5,-153 159.5,-355 453,-355 453,-153 159.5,-153"/></g><g id="clust2" class="cluster"><title>cluster_1</title><polygon fill="none" stroke="grey" points="159.5,-8 159.5,-93 211.5,-93 211.5,-8 159.5,-8"/></g><g id="clust3" class="cluster"><title>cluster_2</title><polygon fill="none" stroke="red" points="30,-110 30,-195 82,-195 82,-110 30,-110"/></g><!-- I --><!-- 0 --><g id="node2" class="node"><title>0</title><ellipse fill="#ffffaa" stroke="black" cx="56" cy="-136" rx="18" ry="18"/><text text-anchor="middle" x="56" y="-132.3" font-family="Lato" font-size="14.00">0</text></g><!-- I&#45;&gt;0 --><g id="edge1" class="edge"><title>I&#45;&gt;0</title><path fill="none" stroke="black" d="M1.15,-136C2.79,-136 17.15,-136 30.63,-136"/><polygon fill="black" stroke="black" points="37.94,-136 30.94,-139.15 34.44,-136 30.94,-136 30.94,-136 30.94,-136 34.44,-136 30.94,-132.85 37.94,-136 37.94,-136"/></g><!-- 0&#45;&gt;0 --><g id="edge2" class="edge"><title>0&#45;&gt;0</title><path fill="none" stroke="black" d="M49.62,-153.04C48.32,-162.86 50.45,-172 56,-172 60.17,-172 62.4,-166.86 62.71,-160.14"/><polygon fill="black" stroke="black" points="62.38,-153.04 65.85,-159.88 62.54,-156.53 62.71,-160.03 62.71,-160.03 62.71,-160.03 62.54,-156.53 59.56,-160.18 62.38,-153.04 62.38,-153.04"/><text text-anchor="start" x="38" y="-175.8" font-family="Lato" font-size="14.00">a &amp; 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!b</text></g><!-- 1&#45;&gt;1 --><g id="edge7" class="edge"><title>1&#45;&gt;1</title><path fill="none" stroke="black" d="M174.79,-259.79C171.31,-270.42 174.88,-281 185.5,-281 193.63,-281 197.63,-274.8 197.5,-267.12"/><polygon fill="black" stroke="black" points="196.21,-259.79 200.52,-266.14 196.81,-263.24 197.42,-266.69 197.42,-266.69 197.42,-266.69 196.81,-263.24 194.32,-267.23 196.21,-259.79 196.21,-259.79"/><text text-anchor="start" x="169.5" y="-299.8" font-family="Lato" font-size="14.00">c &amp; d</text><text text-anchor="start" x="177.5" y="-284.8" font-family="Lato" font-size="14.00" fill="#1f78b4">⓿</text></g><!-- 1&#45;&gt;2 --><g id="edge8" class="edge"><title>1&#45;&gt;2</title><path fill="none" stroke="black" d="M193.27,-228.64C199.09,-216.75 208.65,-201.34 222,-193 243.63,-179.49 273.25,-177.06 293.85,-177.34"/><polygon fill="black" stroke="black" points="301,-177.54 293.91,-180.49 297.5,-177.44 294,-177.34 294,-177.34 294,-177.34 297.5,-177.44 294.09,-174.19 301,-177.54 301,-177.54"/><text text-anchor="start" x="246.5" y="-211.8" font-family="Lato" font-size="14.00">!d</text><text text-anchor="start" x="244.5" y="-196.8" font-family="Lato" font-size="14.00" fill="#1f78b4">⓿</text></g><!-- 1&#45;&gt;3 --><g id="edge9" class="edge"><title>1&#45;&gt;3</title><path fill="none" stroke="black" d="M201.57,-253.49C207.7,-256.49 214.99,-259.49 222,-261 248.51,-266.7 256.26,-265.45 283,-261 327.15,-253.65 375.94,-234.34 403.59,-222.28"/><polygon fill="black" stroke="black" points="410.15,-219.38 405.03,-225.09 406.95,-220.79 403.75,-222.21 403.75,-222.21 403.75,-222.21 406.95,-220.79 402.48,-219.33 410.15,-219.38 410.15,-219.38"/><text text-anchor="start" x="301" y="-274.8" font-family="Lato" font-size="14.00">!c &amp; 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d</text></g><!-- 3&#45;&gt;1 --><g id="edge13" class="edge"><title>3&#45;&gt;1</title><path fill="none" stroke="black" d="M415.53,-226.04C400.55,-244.81 371.04,-277.2 337,-290 291.2,-307.23 235.67,-278.2 206.55,-259.29"/><polygon fill="black" stroke="black" points="200.41,-255.2 207.98,-256.46 203.32,-257.14 206.23,-259.08 206.23,-259.08 206.23,-259.08 203.32,-257.14 204.48,-261.71 200.41,-255.2 200.41,-255.2"/><text text-anchor="start" x="315.5" y="-298.8" font-family="Lato" font-size="14.00">c</text></g><!-- 3&#45;&gt;3 --><g id="edge14" class="edge"><title>3&#45;&gt;3</title><path fill="none" stroke="black" d="M417.77,-227.54C415.17,-237.91 418.25,-248 427,-248 433.7,-248 437.08,-242.08 437.12,-234.66"/><polygon fill="black" stroke="black" points="436.23,-227.54 440.23,-234.1 436.67,-231.01 437.1,-234.49 437.1,-234.49 437.1,-234.49 436.67,-231.01 433.98,-234.88 436.23,-227.54 436.23,-227.54"/><text text-anchor="start" x="421.5" y="-251.8" font-family="Lato" font-size="14.00">!c</text></g><!-- 4&#45;&gt;4 --><g id="edge15" class="edge"><title>4&#45;&gt;4</title><path fill="none" stroke="black" d="M174.79,-48.79C171.31,-59.42 174.88,-70 185.5,-70 193.63,-70 197.63,-63.8 197.5,-56.12"/><polygon fill="black" stroke="black" points="196.21,-48.79 200.52,-55.14 196.81,-52.24 197.42,-55.69 197.42,-55.69 197.42,-55.69 196.81,-52.24 194.32,-56.23 196.21,-48.79 196.21,-48.79"/><text text-anchor="middle" x="185.5" y="-73.8" font-family="Lato" font-size="14.00">1</text></g></g></svg>)
<spot.jupyter.SVG object>
%% Cell type:markdown id: tags:
The `translate()` function can also be called with a formula object. Either as a function, or as a method.
%% Cell type:code id: tags:
``` python
f = spot.formula('a U b'); f
```
%%%% Output: execute_result
$a \mathbin{\mathsf{U}} b$
spot.formula("a U b")
%% Cell type:code id: tags:
``` python
spot.translate(f)
```
%%%% Output: execute_result
![](data:image/svg+xml;utf8,<?xml version="1.0" encoding="UTF-8" standalone="no"?><!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN""http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd"><!-- Generated by graphviz version 2.43.0 (0)--><!-- Pages: 1 --><svg width="170pt" height="125pt"viewBox="0.00 0.00 170.00 124.80" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g id="graph0" class="graph" transform="scale(1.0 1.0) rotate(0) translate(4 120.8)"><polygon fill="white" stroke="transparent" points="-4,4 -4,-120.8 166,-120.8 166,4 -4,4"/><text text-anchor="start" x="59.5" y="-86.6" font-family="Lato" font-size="14.00">[Büchi]</text><!-- I --><!-- 1 --><g id="node2" class="node"><title>1</title><ellipse fill="#ffffaa" stroke="black" cx="56" cy="-22" rx="18" ry="18"/><text text-anchor="middle" x="56" y="-18.3" font-family="Lato" font-size="14.00">1</text></g><!-- I&#45;&gt;1 --><g id="edge1" class="edge"><title>I&#45;&gt;1</title><path fill="none" stroke="black" d="M1.15,-22C2.79,-22 17.15,-22 30.63,-22"/><polygon fill="black" stroke="black" points="37.94,-22 30.94,-25.15 34.44,-22 30.94,-22 30.94,-22 30.94,-22 34.44,-22 30.94,-18.85 37.94,-22 37.94,-22"/></g><!-- 1&#45;&gt;1 --><g id="edge4" class="edge"><title>1&#45;&gt;1</title><path fill="none" stroke="black" d="M49.62,-39.04C48.32,-48.86 50.45,-58 56,-58 60.17,-58 62.4,-52.86 62.71,-46.14"/><polygon fill="black" stroke="black" points="62.38,-39.04 65.85,-45.88 62.54,-42.53 62.71,-46.03 62.71,-46.03 62.71,-46.03 62.54,-42.53 59.56,-46.18 62.38,-39.04 62.38,-39.04"/><text text-anchor="start" x="38" y="-61.8" font-family="Lato" font-size="14.00">a &amp; !b</text></g><!-- 0 --><g id="node3" class="node"><title>0</title><ellipse fill="#ffffaa" stroke="black" cx="140" cy="-22" rx="18" ry="18"/><ellipse fill="none" stroke="black" cx="140" cy="-22" rx="22" ry="22"/><text text-anchor="middle" x="140" y="-18.3" font-family="Lato" font-size="14.00">0</text></g><!-- 1&#45;&gt;0 --><g id="edge3" class="edge"><title>1&#45;&gt;0</title><path fill="none" stroke="black" d="M74.39,-22C84.9,-22 98.55,-22 110.6,-22"/><polygon fill="black" stroke="black" points="117.85,-22 110.85,-25.15 114.35,-22 110.85,-22 110.85,-22 110.85,-22 114.35,-22 110.85,-18.85 117.85,-22 117.85,-22"/><text text-anchor="start" x="92" y="-25.8" font-family="Lato" font-size="14.00">b</text></g><!-- 0&#45;&gt;0 --><g id="edge2" class="edge"><title>0&#45;&gt;0</title><path fill="none" stroke="black" d="M131.99,-42.58C130.89,-52.84 133.55,-62 140,-62 144.83,-62 147.54,-56.85 148.13,-49.95"/><polygon fill="black" stroke="black" points="148.01,-42.58 151.27,-49.53 148.06,-46.08 148.12,-49.58 148.12,-49.58 148.12,-49.58 148.06,-46.08 144.97,-49.63 148.01,-42.58 148.01,-42.58"/><text text-anchor="middle" x="140" y="-65.8" font-family="Lato" font-size="14.00">1</text></g></g></svg>)
<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7f9f5d7cf480> >
<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7f37382c09f0> >
%% Cell type:code id: tags:
``` python
f.translate()
```
%%%% Output: execute_result
![](data:image/svg+xml;utf8,<?xml version="1.0" encoding="UTF-8" standalone="no"?><!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN""http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd"><!-- Generated by graphviz version 2.43.0 (0)--><!-- Pages: 1 --><svg width="170pt" height="125pt"viewBox="0.00 0.00 170.00 124.80" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g id="graph0" class="graph" transform="scale(1.0 1.0) rotate(0) translate(4 120.8)"><polygon fill="white" stroke="transparent" points="-4,4 -4,-120.8 166,-120.8 166,4 -4,4"/><text text-anchor="start" x="59.5" y="-86.6" font-family="Lato" font-size="14.00">[Büchi]</text><!-- I --><!-- 1 --><g id="node2" class="node"><title>1</title><ellipse fill="#ffffaa" stroke="black" cx="56" cy="-22" rx="18" ry="18"/><text text-anchor="middle" x="56" y="-18.3" font-family="Lato" font-size="14.00">1</text></g><!-- I&#45;&gt;1 --><g id="edge1" class="edge"><title>I&#45;&gt;1</title><path fill="none" stroke="black" d="M1.15,-22C2.79,-22 17.15,-22 30.63,-22"/><polygon fill="black" stroke="black" points="37.94,-22 30.94,-25.15 34.44,-22 30.94,-22 30.94,-22 30.94,-22 34.44,-22 30.94,-18.85 37.94,-22 37.94,-22"/></g><!-- 1&#45;&gt;1 --><g id="edge4" class="edge"><title>1&#45;&gt;1</title><path fill="none" stroke="black" d="M49.62,-39.04C48.32,-48.86 50.45,-58 56,-58 60.17,-58 62.4,-52.86 62.71,-46.14"/><polygon fill="black" stroke="black" points="62.38,-39.04 65.85,-45.88 62.54,-42.53 62.71,-46.03 62.71,-46.03 62.71,-46.03 62.54,-42.53 59.56,-46.18 62.38,-39.04 62.38,-39.04"/><text text-anchor="start" x="38" y="-61.8" font-family="Lato" font-size="14.00">a &amp; !b</text></g><!-- 0 --><g id="node3" class="node"><title>0</title><ellipse fill="#ffffaa" stroke="black" cx="140" cy="-22" rx="18" ry="18"/><ellipse fill="none" stroke="black" cx="140" cy="-22" rx="22" ry="22"/><text text-anchor="middle" x="140" y="-18.3" font-family="Lato" font-size="14.00">0</text></g><!-- 1&#45;&gt;0 --><g id="edge3" class="edge"><title>1&#45;&gt;0</title><path fill="none" stroke="black" d="M74.39,-22C84.9,-22 98.55,-22 110.6,-22"/><polygon fill="black" stroke="black" points="117.85,-22 110.85,-25.15 114.35,-22 110.85,-22 110.85,-22 110.85,-22 114.35,-22 110.85,-18.85 117.85,-22 117.85,-22"/><text text-anchor="start" x="92" y="-25.8" font-family="Lato" font-size="14.00">b</text></g><!-- 0&#45;&gt;0 --><g id="edge2" class="edge"><title>0&#45;&gt;0</title><path fill="none" stroke="black" d="M131.99,-42.58C130.89,-52.84 133.55,-62 140,-62 144.83,-62 147.54,-56.85 148.13,-49.95"/><polygon fill="black" stroke="black" points="148.01,-42.58 151.27,-49.53 148.06,-46.08 148.12,-49.58 148.12,-49.58 148.12,-49.58 148.06,-46.08 144.97,-49.63 148.01,-42.58 148.01,-42.58"/><text text-anchor="middle" x="140" y="-65.8" font-family="Lato" font-size="14.00">1</text></g></g></svg>)
<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7f9f5d7cfc00> >
<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7f37382c00f0> >
%% Cell type:markdown id: tags:
When used as a method, all the arguments are translation options. Here is a monitor:
%% Cell type:code id: tags:
``` python
f.translate('mon')
```
%%%% Output: execute_result
![](data:image/svg+xml;utf8,<?xml version="1.0" encoding="UTF-8" standalone="no"?><!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN""http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd"><!-- Generated by graphviz version 2.43.0 (0)--><!-- Pages: 1 --><svg width="162pt" height="115pt"viewBox="0.00 0.00 162.00 115.00" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g id="graph0" class="graph" transform="scale(1.0 1.0) rotate(0) translate(4 111)"><polygon fill="white" stroke="transparent" points="-4,4 -4,-111 158,-111 158,4 -4,4"/><text text-anchor="start" x="74" y="-91.8" font-family="Lato" font-size="14.00">t</text><text text-anchor="start" x="66" y="-76.8" font-family="Lato" font-size="14.00">[all]</text><!-- I --><!-- 1 --><g id="node2" class="node"><title>1</title><ellipse fill="#ffffaa" stroke="black" cx="56" cy="-18" rx="18" ry="18"/><text text-anchor="middle" x="56" y="-14.3" font-family="Lato" font-size="14.00">1</text></g><!-- I&#45;&gt;1 --><g id="edge1" class="edge"><title>I&#45;&gt;1</title><path fill="none" stroke="black" d="M1.15,-18C2.79,-18 17.15,-18 30.63,-18"/><polygon fill="black" stroke="black" points="37.94,-18 30.94,-21.15 34.44,-18 30.94,-18 30.94,-18 30.94,-18 34.44,-18 30.94,-14.85 37.94,-18 37.94,-18"/></g><!-- 1&#45;&gt;1 --><g id="edge4" class="edge"><title>1&#45;&gt;1</title><path fill="none" stroke="black" d="M49.62,-35.04C48.32,-44.86 50.45,-54 56,-54 60.17,-54 62.4,-48.86 62.71,-42.14"/><polygon fill="black" stroke="black" points="62.38,-35.04 65.85,-41.88 62.54,-38.53 62.71,-42.03 62.71,-42.03 62.71,-42.03 62.54,-38.53 59.56,-42.18 62.38,-35.04 62.38,-35.04"/><text text-anchor="start" x="38" y="-57.8" font-family="Lato" font-size="14.00">a &amp; !b</text></g><!-- 0 --><g id="node3" class="node"><title>0</title><ellipse fill="#ffffaa" stroke="black" cx="136" cy="-18" rx="18" ry="18"/><text text-anchor="middle" x="136" y="-14.3" font-family="Lato" font-size="14.00">0</text></g><!-- 1&#45;&gt;0 --><g id="edge3" class="edge"><title>1&#45;&gt;0</title><path fill="none" stroke="black" d="M74.31,-18C85.02,-18 98.92,-18 110.71,-18"/><polygon fill="black" stroke="black" points="117.74,-18 110.74,-21.15 114.24,-18 110.74,-18 110.74,-18 110.74,-18 114.24,-18 110.74,-14.85 117.74,-18 117.74,-18"/><text text-anchor="start" x="92" y="-21.8" font-family="Lato" font-size="14.00">b</text></g><!-- 0&#45;&gt;0 --><g id="edge2" class="edge"><title>0&#45;&gt;0</title><path fill="none" stroke="black" d="M128.97,-34.66C127.41,-44.62 129.75,-54 136,-54 140.69,-54 143.18,-48.73 143.47,-41.89"/><polygon fill="black" stroke="black" points="143.03,-34.66 146.6,-41.46 143.24,-38.16 143.46,-41.65 143.46,-41.65 143.46,-41.65 143.24,-38.16 140.31,-41.84 143.03,-34.66 143.03,-34.66"/><text text-anchor="middle" x="136" y="-57.8" font-family="Lato" font-size="14.00">1</text></g></g></svg>)
<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7f9f5d7cf3f0> >
<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7f37382c0c00> >
%% Cell type:markdown id: tags:
The following three cells show a formulas for which it makes a difference to select `'small'` or `'deterministic'`.
%% Cell type:code id: tags:
``` python
f = spot.formula('Ga | Gb | Gc'); f
```
%%%% Output: execute_result
$\mathsf{G} a \lor \mathsf{G} b \lor \mathsf{G} c$
spot.formula("Ga | Gb | Gc")
%% Cell type:code id: tags:
``` python
f.translate('ba', 'small').show('.v')
```
%%%% Output: execute_result
![](data:image/svg+xml;utf8,<?xml version="1.0" encoding="UTF-8" standalone="no"?><!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN""http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd"><!-- Generated by graphviz version 2.43.0 (0)--><!-- Pages: 1 --><svg width="252pt" height="217pt"viewBox="0.00 0.00 252.00 216.80" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g id="graph0" class="graph" transform="scale(1.0 1.0) rotate(0) translate(4 212.8)"><polygon fill="white" stroke="transparent" points="-4,4 -4,-212.8 248,-212.8 248,4 -4,4"/><text text-anchor="start" x="100.5" y="-178.6" font-family="Lato" font-size="14.00">[Büchi]</text><!-- I --><!-- 0 --><g id="node2" class="node"><title>0</title><ellipse fill="#ffffaa" stroke="black" cx="109" cy="-113" rx="18" ry="18"/><text text-anchor="middle" x="109" y="-109.3" font-family="Lato" font-size="14.00">0</text></g><!-- I&#45;&gt;0 --><g id="edge1" class="edge"><title>I&#45;&gt;0</title><path fill="none" stroke="black" d="M109,-167.85C109,-166.21 109,-151.85 109,-138.37"/><polygon fill="black" stroke="black" points="109,-131.06 112.15,-138.06 109,-134.56 109,-138.06 109,-138.06 109,-138.06 109,-134.56 105.85,-138.06 109,-131.06 109,-131.06"/></g><!-- 1 --><g id="node3" class="node"><title>1</title><ellipse fill="#ffffaa" stroke="black" cx="22" cy="-22" rx="18" ry="18"/><ellipse fill="none" stroke="black" cx="22" cy="-22" rx="22" ry="22"/><text text-anchor="middle" x="22" y="-18.3" font-family="Lato" font-size="14.00">1</text></g><!-- 0&#45;&gt;1 --><g id="edge2" class="edge"><title>0&#45;&gt;1</title><path fill="none" stroke="black" d="M96.9,-99.62C82.69,-85.08 58.89,-60.73 41.93,-43.39"/><polygon fill="black" stroke="black" points="36.91,-38.25 44.05,-41.05 39.35,-40.75 41.8,-43.25 41.8,-43.25 41.8,-43.25 39.35,-40.75 39.55,-45.46 36.91,-38.25 36.91,-38.25"/><text text-anchor="start" x="74" y="-65.8" font-family="Lato" font-size="14.00">a</text></g><!-- 2 --><g id="node4" class="node"><title>2</title><ellipse fill="#ffffaa" stroke="black" cx="109" cy="-22" rx="18" ry="18"/><ellipse fill="none" stroke="black" cx="109" cy="-22" rx="22" ry="22"/><text text-anchor="middle" x="109" y="-18.3" font-family="Lato" font-size="14.00">2</text></g><!-- 0&#45;&gt;2 --><g id="edge3" class="edge"><title>0&#45;&gt;2</title><path fill="none" stroke="black" d="M109,-94.84C109,-82.54 109,-65.68 109,-51.39"/><polygon fill="black" stroke="black" points="109,-44.19 112.15,-51.19 109,-47.69 109,-51.19 109,-51.19 109,-51.19 109,-47.69 105.85,-51.19 109,-44.19 109,-44.19"/><text text-anchor="start" x="109" y="-65.8" font-family="Lato" font-size="14.00">b</text></g><!-- 3 --><g id="node5" class="node"><title>3</title><ellipse fill="#ffffaa" stroke="black" cx="197" cy="-22" rx="18" ry="18"/><ellipse fill="none" stroke="black" cx="197" cy="-22" rx="22" ry="22"/><text text-anchor="middle" x="197" y="-18.3" font-family="Lato" font-size="14.00">3</text></g><!-- 0&#45;&gt;3 --><g id="edge4" class="edge"><title>0&#45;&gt;3</title><path fill="none" stroke="black" d="M121.24,-99.62C135.62,-85.08 159.69,-60.73 176.84,-43.39"/><polygon fill="black" stroke="black" points="181.92,-38.25 179.24,-45.44 179.46,-40.74 177,-43.23 177,-43.23 177,-43.23 179.46,-40.74 174.76,-41.01 181.92,-38.25 181.92,-38.25"/><text text-anchor="start" x="158" y="-65.8" font-family="Lato" font-size="14.00">c</text></g><!-- 1&#45;&gt;1 --><g id="edge5" class="edge"><title>1&#45;&gt;1</title><path fill="none" stroke="black" d="M42.58,-30.37C52.84,-31.53 62,-28.74 62,-22 62,-16.95 56.85,-14.11 49.95,-13.5"/><polygon fill="black" stroke="black" points="42.58,-13.63 49.52,-10.36 46.08,-13.57 49.58,-13.51 49.58,-13.51 49.58,-13.51 46.08,-13.57 49.63,-16.66 42.58,-13.63 42.58,-13.63"/><text text-anchor="start" x="62" y="-18.3" font-family="Lato" font-size="14.00">a</text></g><!-- 2&#45;&gt;2 --><g id="edge6" class="edge"><title>2&#45;&gt;2</title><path fill="none" stroke="black" d="M129.58,-30.37C139.84,-31.53 149,-28.74 149,-22 149,-16.95 143.85,-14.11 136.95,-13.5"/><polygon fill="black" stroke="black" points="129.58,-13.63 136.52,-10.36 133.08,-13.57 136.58,-13.51 136.58,-13.51 136.58,-13.51 133.08,-13.57 136.63,-16.66 129.58,-13.63 129.58,-13.63"/><text text-anchor="start" x="149" y="-18.3" font-family="Lato" font-size="14.00">b</text></g><!-- 3&#45;&gt;3 --><g id="edge7" class="edge"><title>3&#45;&gt;3</title><path fill="none" stroke="black" d="M217.58,-30.37C227.84,-31.53 237,-28.74 237,-22 237,-16.95 231.85,-14.11 224.95,-13.5"/><polygon fill="black" stroke="black" points="217.58,-13.63 224.52,-10.36 221.08,-13.57 224.58,-13.51 224.58,-13.51 224.58,-13.51 221.08,-13.57 224.63,-16.66 217.58,-13.63 217.58,-13.63"/><text text-anchor="start" x="237" y="-18.3" font-family="Lato" font-size="14.00">c</text></g></g></svg>)
<spot.jupyter.SVG object>
%% Cell type:code id: tags:
``` python
f.translate('ba', 'det').show('v.')
```
%%%% Output: execute_result
![](data:image/svg+xml;utf8,<?xml version="1.0" encoding="UTF-8" standalone="no"?><!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN""http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd"><!-- Generated by graphviz version 2.43.0 (0)--><!-- Pages: 1 --><svg width="586pt" height="320pt"viewBox="0.00 0.00 585.88 319.80" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g id="graph0" class="graph" transform="scale(1.0 1.0) rotate(0) translate(4 315.8)"><polygon fill="white" stroke="transparent" points="-4,4 -4,-315.8 581.88,-315.8 581.88,4 -4,4"/><text text-anchor="start" x="267.44" y="-281.6" font-family="Lato" font-size="14.00">[Büchi]</text><!-- I --><!-- 6 --><g id="node2" class="node"><title>6</title><ellipse fill="#ffffaa" stroke="black" cx="283.88" cy="-212" rx="18" ry="18"/><ellipse fill="none" stroke="black" cx="283.88" cy="-212" rx="22" ry="22"/><text text-anchor="middle" x="283.88" y="-208.3" font-family="Lato" font-size="14.00">6</text></g><!-- I&#45;&gt;6 --><g id="edge1" class="edge"><title>I&#45;&gt;6</title><path fill="none" stroke="black" d="M283.88,-270.83C283.88,-269.16 283.88,-255.12 283.88,-241.29"/><polygon fill="black" stroke="black" points="283.88,-234.14 287.03,-241.14 283.88,-237.64 283.88,-241.14 283.88,-241.14 283.88,-241.14 283.88,-237.64 280.73,-241.14 283.88,-234.14 283.88,-234.14"/></g><!-- 6&#45;&gt;6 --><g id="edge20" class="edge"><title>6&#45;&gt;6</title><path fill="none" stroke="black" d="M304.87,-219.32C314.97,-220.22 323.88,-217.78 323.88,-212 323.88,-207.66 318.87,-205.21 312.1,-204.63"/><polygon fill="black" stroke="black" points="304.87,-204.68 311.85,-201.48 308.37,-204.66 311.87,-204.63 311.87,-204.63 311.87,-204.63 308.37,-204.66 311.9,-207.78 304.87,-204.68 304.87,-204.68"/><text text-anchor="start" x="323.88" y="-208.3" font-family="Lato" font-size="14.00">a &amp; b &amp; c</text></g><!-- 0 --><g id="node3" class="node"><title>0</title><ellipse fill="#ffffaa" stroke="black" cx="96.88" cy="-22" rx="18" ry="18"/><ellipse fill="none" stroke="black" cx="96.88" cy="-22" rx="22" ry="22"/><text text-anchor="middle" x="96.88" y="-18.3" font-family="Lato" font-size="14.00">0</text></g><!-- 6&#45;&gt;0 --><g id="edge14" class="edge"><title>6&#45;&gt;0</title><path fill="none" stroke="black" d="M261.73,-208.65C201.89,-201.81 39.37,-179.75 7.88,-139 -20.31,-102.5 36.35,-59.38 71.61,-37.42"/><polygon fill="black" stroke="black" points="77.93,-33.57 73.59,-39.91 74.94,-35.4 71.95,-37.22 71.95,-37.22 71.95,-37.22 74.94,-35.4 70.31,-34.53 77.93,-33.57 77.93,-33.57"/><text text-anchor="start" x="7.88" y="-113.3" font-family="Lato" font-size="14.00">!a &amp; !b &amp; c</text></g><!-- 1 --><g id="node4" class="node"><title>1</title><ellipse fill="#ffffaa" stroke="black" cx="471.88" cy="-22" rx="18" ry="18"/><ellipse fill="none" stroke="black" cx="471.88" cy="-22" rx="22" ry="22"/><text text-anchor="middle" x="471.88" y="-18.3" font-family="Lato" font-size="14.00">1</text></g><!-- 6&#45;&gt;1 --><g id="edge15" class="edge"><title>6&#45;&gt;1</title><path fill="none" stroke="black" d="M306.14,-211.9C353.18,-212.4 462.08,-205.94 506.88,-139 526.19,-110.15 506.06,-70.3 489.32,-45.61"/><polygon fill="black" stroke="black" points="485.16,-39.68 491.76,-43.6 487.17,-42.54 489.18,-45.41 489.18,-45.41 489.18,-45.41 487.17,-42.54 486.6,-47.22 485.16,-39.68 485.16,-39.68"/><text text-anchor="start" x="513.88" y="-113.3" font-family="Lato" font-size="14.00">a &amp; !b &amp; !c</text></g><!-- 2 --><g id="node5" class="node"><title>2</title><ellipse fill="#ffffaa" stroke="black" cx="321.88" cy="-22" rx="18" ry="18"/><ellipse fill="none" stroke="black" cx="321.88" cy="-22" rx="22" ry="22"/><text text-anchor="middle" x="321.88" y="-18.3" font-family="Lato" font-size="14.00">2</text></g><!-- 6&#45;&gt;2 --><g id="edge16" class="edge"><title>6&#45;&gt;2</title><path fill="none" stroke="black" d="M296.7,-193.99C300.98,-187.44 305.31,-179.69 307.88,-172 321.33,-131.79 323.32,-82.31 323,-51.71"/><polygon fill="black" stroke="black" points="322.87,-44.35 326.14,-51.3 322.93,-47.85 322.99,-51.35 322.99,-51.35 322.99,-51.35 322.93,-47.85 319.84,-51.4 322.87,-44.35 322.87,-44.35"/><text text-anchor="start" x="320.88" y="-113.3" font-family="Lato" font-size="14.00">!a &amp; b &amp; !c</text></g><!-- 3 --><g id="node6" class="node"><title>3</title><ellipse fill="#ffffaa" stroke="black" cx="102.88" cy="-117" rx="18" ry="18"/><ellipse fill="none" stroke="black" cx="102.88" cy="-117" rx="22" ry="22"/><text text-anchor="middle" x="102.88" y="-113.3" font-family="Lato" font-size="14.00">3</text></g><!-- 6&#45;&gt;3 --><g id="edge17" class="edge"><title>6&#45;&gt;3</title><path fill="none" stroke="black" d="M262.8,-205.63C240.04,-199.36 203.12,-187.8 173.88,-172 156,-162.34 137.79,-148.39 124.29,-137.09"/><polygon fill="black" stroke="black" points="118.81,-132.43 126.18,-134.56 121.48,-134.69 124.14,-136.96 124.14,-136.96 124.14,-136.96 121.48,-134.69 122.1,-139.36 118.81,-132.43 118.81,-132.43"/><text text-anchor="start" x="173.88" y="-160.8" font-family="Lato" font-size="14.00">!a &amp; b &amp; c</text></g><!-- 4 --><g id="node7" class="node"><title>4</title><ellipse fill="#ffffaa" stroke="black" cx="214.88" cy="-117" rx="18" ry="18"/><ellipse fill="none" stroke="black" cx="214.88" cy="-117" rx="22" ry="22"/><text text-anchor="middle" x="214.88" y="-113.3" font-family="Lato" font-size="14.00">4</text></g><!-- 6&#45;&gt;4 --><g id="edge18" class="edge"><title>6&#45;&gt;4</title><path fill="none" stroke="black" d="M268.43,-195.68C261.77,-188.73 254.1,-180.23 247.88,-172 241,-162.88 234.26,-152.26 228.69,-142.86"/><polygon fill="black" stroke="black" points="225.03,-136.58 231.27,-141.05 226.79,-139.61 228.55,-142.63 228.55,-142.63 228.55,-142.63 226.79,-139.61 225.83,-144.22 225.03,-136.58 225.03,-136.58"/><text text-anchor="start" x="247.88" y="-160.8" font-family="Lato" font-size="14.00">a &amp; !b &amp; c</text></g><!-- 5 --><g id="node8" class="node"><title>5</title><ellipse fill="#ffffaa" stroke="black" cx="425.88" cy="-117" rx="18" ry="18"/><ellipse fill="none" stroke="black" cx="425.88" cy="-117" rx="22" ry="22"/><text text-anchor="middle" x="425.88" y="-113.3" font-family="Lato" font-size="14.00">5</text></g><!-- 6&#45;&gt;5 --><g id="edge19" class="edge"><title>6&#45;&gt;5</title><path fill="none" stroke="black" d="M301.87,-199.22C327.12,-182.68 373.17,-152.52 401.49,-133.98"/><polygon fill="black" stroke="black" points="407.6,-129.98 403.47,-136.45 404.67,-131.89 401.74,-133.81 401.74,-133.81 401.74,-133.81 404.67,-131.89 400.02,-131.18 407.6,-129.98 407.6,-129.98"/><text text-anchor="start" x="362.88" y="-160.8" font-family="Lato" font-size="14.00">a &amp; b &amp; !c</text></g><!-- 0&#45;&gt;0 --><g id="edge2" class="edge"><title>0&#45;&gt;0</title><path fill="none" stroke="black" d="M117.46,-30.37C127.73,-31.53 136.88,-28.74 136.88,-22 136.88,-16.95 131.73,-14.11 124.83,-13.5"/><polygon fill="black" stroke="black" points="117.46,-13.63 124.41,-10.36 120.96,-13.57 124.46,-13.51 124.46,-13.51 124.46,-13.51 120.96,-13.57 124.52,-16.66 117.46,-13.63 117.46,-13.63"/><text text-anchor="start" x="136.88" y="-18.3" font-family="Lato" font-size="14.00">c</text></g><!-- 1&#45;&gt;1 --><g id="edge3" class="edge"><title>1&#45;&gt;1</title><path fill="none" stroke="black" d="M492.46,-30.37C502.73,-31.53 511.88,-28.74 511.88,-22 511.88,-16.95 506.73,-14.11 499.83,-13.5"/><polygon fill="black" stroke="black" points="492.46,-13.63 499.41,-10.36 495.96,-13.57 499.46,-13.51 499.46,-13.51 499.46,-13.51 495.96,-13.57 499.52,-16.66 492.46,-13.63 492.46,-13.63"/><text text-anchor="start" x="511.88" y="-18.3" font-family="Lato" font-size="14.00">a</text></g><!-- 2&#45;&gt;2 --><g id="edge4" class="edge"><title>2&#45;&gt;2</title><path fill="none" stroke="black" d="M342.46,-30.37C352.73,-31.53 361.88,-28.74 361.88,-22 361.88,-16.95 356.73,-14.11 349.83,-13.5"/><polygon fill="black" stroke="black" points="342.46,-13.63 349.41,-10.36 345.96,-13.57 349.46,-13.51 349.46,-13.51 349.46,-13.51 345.96,-13.57 349.52,-16.66 342.46,-13.63 342.46,-13.63"/><text text-anchor="start" x="361.88" y="-18.3" font-family="Lato" font-size="14.00">b</text></g><!-- 3&#45;&gt;0 --><g id="edge5" class="edge"><title>3&#45;&gt;0</title><path fill="none" stroke="black" d="M99.76,-94.99C99.02,-89.18 98.31,-82.85 97.88,-77 97.27,-68.61 96.96,-59.47 96.82,-51.13"/><polygon fill="black" stroke="black" points="96.74,-44.05 99.97,-51.02 96.78,-47.55 96.82,-51.05 96.82,-51.05 96.82,-51.05 96.78,-47.55 93.67,-51.09 96.74,-44.05 96.74,-44.05"/><text text-anchor="start" x="97.88" y="-65.8" font-family="Lato" font-size="14.00">!b &amp; c</text></g><!-- 3&#45;&gt;2 --><g id="edge6" class="edge"><title>3&#45;&gt;2</title><path fill="none" stroke="black" d="M116.32,-99.46C128.01,-85.47 144.37,-66.93 152.88,-62 197.27,-36.27 257.43,-27.51 292.71,-24.54"/><polygon fill="black" stroke="black" points="299.85,-23.98 293.11,-27.66 296.36,-24.25 292.87,-24.52 292.87,-24.52 292.87,-24.52 296.36,-24.25 292.63,-21.38 299.85,-23.98 299.85,-23.98"/><text text-anchor="start" x="152.88" y="-65.8" font-family="Lato" font-size="14.00">b &amp; !c</text></g><!-- 3&#45;&gt;3 --><g id="edge7" class="edge"><title>3&#45;&gt;3</title><path fill="none" stroke="black" d="M123.46,-125.37C133.73,-126.53 142.88,-123.74 142.88,-117 142.88,-111.95 137.73,-109.11 130.83,-108.5"/><polygon fill="black" stroke="black" points="123.46,-108.63 130.41,-105.36 126.96,-108.57 130.46,-108.51 130.46,-108.51 130.46,-108.51 126.96,-108.57 130.52,-111.66 123.46,-108.63 123.46,-108.63"/><text text-anchor="start" x="142.88" y="-113.3" font-family="Lato" font-size="14.00">b &amp; c</text></g><!-- 4&#45;&gt;0 --><g id="edge8" class="edge"><title>4&#45;&gt;0</title><path fill="none" stroke="black" d="M210.61,-95.34C207.38,-84.24 201.91,-71.01 192.88,-62 174.59,-43.72 146.57,-33.68 125.52,-28.38"/><polygon fill="black" stroke="black" points="118.67,-26.76 126.21,-25.3 122.07,-27.56 125.48,-28.37 125.48,-28.37 125.48,-28.37 122.07,-27.56 124.76,-31.43 118.67,-26.76 118.67,-26.76"/><text text-anchor="start" x="202.88" y="-65.8" font-family="Lato" font-size="14.00">!a &amp; c</text></g><!-- 4&#45;&gt;1 --><g id="edge9" class="edge"><title>4&#45;&gt;1</title><path fill="none" stroke="black" d="M235.16,-107.56C261.77,-96.58 310.02,-77.04 351.88,-62 383.22,-50.74 419.65,-39.11 444.07,-31.51"/><polygon fill="black" stroke="black" points="450.94,-29.38 445.19,-34.46 447.6,-30.42 444.25,-31.45 444.25,-31.45 444.25,-31.45 447.6,-30.42 443.32,-28.44 450.94,-29.38 450.94,-29.38"/><text text-anchor="start" x="351.88" y="-65.8" font-family="Lato" font-size="14.00">a &amp; !c</text></g><!-- 4&#45;&gt;4 --><g id="edge10" class="edge"><title>4&#45;&gt;4</title><path fill="none" stroke="black" d="M235.46,-125.37C245.73,-126.53 254.88,-123.74 254.88,-117 254.88,-111.95 249.73,-109.11 242.83,-108.5"/><polygon fill="black" stroke="black" points="235.46,-108.63 242.41,-105.36 238.96,-108.57 242.46,-108.51 242.46,-108.51 242.46,-108.51 238.96,-108.57 242.52,-111.66 235.46,-108.63 235.46,-108.63"/><text text-anchor="start" x="254.88" y="-113.3" font-family="Lato" font-size="14.00">a &amp; c</text></g><!-- 5&#45;&gt;1 --><g id="edge11" class="edge"><title>5&#45;&gt;1</title><path fill="none" stroke="black" d="M437.75,-98.1C441.84,-91.59 446.29,-84.09 449.88,-77 454.33,-68.22 458.58,-58.32 462.13,-49.42"/><polygon fill="black" stroke="black" points="464.7,-42.84 465.09,-50.51 463.43,-46.1 462.15,-49.36 462.15,-49.36 462.15,-49.36 463.43,-46.1 459.22,-48.21 464.7,-42.84 464.7,-42.84"/><text text-anchor="start" x="455.88" y="-65.8" font-family="Lato" font-size="14.00">a &amp; !b</text></g><!-- 5&#45;&gt;2 --><g id="edge12" class="edge"><title>5&#45;&gt;2</title><path fill="none" stroke="black" d="M416.48,-96.87C410.32,-85.72 401.46,-71.95 390.88,-62 378.57,-50.41 362.18,-40.96 348.46,-34.27"/><polygon fill="black" stroke="black" points="341.97,-31.21 349.65,-31.34 345.14,-32.7 348.3,-34.19 348.3,-34.19 348.3,-34.19 345.14,-32.7 346.96,-37.04 341.97,-31.21 341.97,-31.21"/><text text-anchor="start" x="402.88" y="-65.8" font-family="Lato" font-size="14.00">!a &amp; b</text></g><!-- 5&#45;&gt;5 --><g id="edge13" class="edge"><title>5&#45;&gt;5</title><path fill="none" stroke="black" d="M446.46,-125.37C456.73,-126.53 465.88,-123.74 465.88,-117 465.88,-111.95 460.73,-109.11 453.83,-108.5"/><polygon fill="black" stroke="black" points="446.46,-108.63 453.41,-105.36 449.96,-108.57 453.46,-108.51 453.46,-108.51 453.46,-108.51 449.96,-108.57 453.52,-111.66 446.46,-108.63 446.46,-108.63"/><text text-anchor="start" x="465.88" y="-113.3" font-family="Lato" font-size="14.00">a &amp; b</text></g></g></svg>)
![](data:image/svg+xml;utf8,<?xml version="1.0" encoding="UTF-8" standalone="no"?><!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN""http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd"><!-- Generated by graphviz version 2.43.0 (0)--><!-- Pages: 1 --><svg width="586pt" height="320pt"viewBox="0.00 0.00 585.88 319.80" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g id="graph0" class="graph" transform="scale(1.0 1.0) rotate(0) translate(4 315.8)"><polygon fill="white" stroke="transparent" points="-4,4 -4,-315.8 581.88,-315.8 581.88,4 -4,4"/><text text-anchor="start" x="267.44" y="-281.6" font-family="Lato" font-size="14.00">[Büchi]</text><!-- I --><!-- 6 --><g id="node2" class="node"><title>6</title><ellipse fill="#ffffaa" stroke="black" cx="283.88" cy="-212" rx="18" ry="18"/><ellipse fill="none" stroke="black" cx="283.88" cy="-212" rx="22" ry="22"/><text text-anchor="middle" x="283.88" y="-208.3" font-family="Lato" font-size="14.00">6</text></g><!-- I&#45;&gt;6 --><g id="edge1" class="edge"><title>I&#45;&gt;6</title><path fill="none" stroke="black" d="M283.88,-270.83C283.88,-269.16 283.88,-255.12 283.88,-241.29"/><polygon fill="black" stroke="black" points="283.88,-234.14 287.03,-241.14 283.88,-237.64 283.88,-241.14 283.88,-241.14 283.88,-241.14 283.88,-237.64 280.73,-241.14 283.88,-234.14 283.88,-234.14"/></g><!-- 6&#45;&gt;6 --><g id="edge20" class="edge"><title>6&#45;&gt;6</title><path fill="none" stroke="black" d="M304.87,-219.32C314.97,-220.22 323.88,-217.78 323.88,-212 323.88,-207.66 318.87,-205.21 312.1,-204.63"/><polygon fill="black" stroke="black" points="304.87,-204.68 311.85,-201.48 308.37,-204.66 311.87,-204.63 311.87,-204.63 311.87,-204.63 308.37,-204.66 311.9,-207.78 304.87,-204.68 304.87,-204.68"/><text text-anchor="start" x="323.88" y="-208.3" font-family="Lato" font-size="14.00">a &amp; b &amp; c</text></g><!-- 0 --><g id="node3" class="node"><title>0</title><ellipse fill="#ffffaa" stroke="black" cx="96.88" cy="-22" rx="18" ry="18"/><ellipse fill="none" stroke="black" cx="96.88" cy="-22" rx="22" ry="22"/><text text-anchor="middle" x="96.88" y="-18.3" font-family="Lato" font-size="14.00">0</text></g><!-- 6&#45;&gt;0 --><g id="edge14" class="edge"><title>6&#45;&gt;0</title><path fill="none" stroke="black" d="M261.73,-208.65C201.89,-201.81 39.37,-179.75 7.88,-139 -20.31,-102.5 36.35,-59.38 71.61,-37.42"/><polygon fill="black" stroke="black" points="77.93,-33.57 73.59,-39.91 74.94,-35.4 71.95,-37.22 71.95,-37.22 71.95,-37.22 74.94,-35.4 70.31,-34.53 77.93,-33.57 77.93,-33.57"/><text text-anchor="start" x="7.88" y="-113.3" font-family="Lato" font-size="14.00">!a &amp; !b &amp; c</text></g><!-- 1 --><g id="node4" class="node"><title>1</title><ellipse fill="#ffffaa" stroke="black" cx="321.88" cy="-22" rx="18" ry="18"/><ellipse fill="none" stroke="black" cx="321.88" cy="-22" rx="22" ry="22"/><text text-anchor="middle" x="321.88" y="-18.3" font-family="Lato" font-size="14.00">1</text></g><!-- 6&#45;&gt;1 --><g id="edge15" class="edge"><title>6&#45;&gt;1</title><path fill="none" stroke="black" d="M296.7,-193.99C300.98,-187.44 305.31,-179.69 307.88,-172 321.33,-131.79 323.32,-82.31 323,-51.71"/><polygon fill="black" stroke="black" points="322.87,-44.35 326.14,-51.3 322.93,-47.85 322.99,-51.35 322.99,-51.35 322.99,-51.35 322.93,-47.85 319.84,-51.4 322.87,-44.35 322.87,-44.35"/><text text-anchor="start" x="320.88" y="-113.3" font-family="Lato" font-size="14.00">!a &amp; b &amp; !c</text></g><!-- 2 --><g id="node5" class="node"><title>2</title><ellipse fill="#ffffaa" stroke="black" cx="471.88" cy="-22" rx="18" ry="18"/><ellipse fill="none" stroke="black" cx="471.88" cy="-22" rx="22" ry="22"/><text text-anchor="middle" x="471.88" y="-18.3" font-family="Lato" font-size="14.00">2</text></g><!-- 6&#45;&gt;2 --><g id="edge16" class="edge"><title>6&#45;&gt;2</title><path fill="none" stroke="black" d="M306.14,-211.9C353.18,-212.4 462.08,-205.94 506.88,-139 526.19,-110.15 506.06,-70.3 489.32,-45.61"/><polygon fill="black" stroke="black" points="485.16,-39.68 491.76,-43.6 487.17,-42.54 489.18,-45.41 489.18,-45.41 489.18,-45.41 487.17,-42.54 486.6,-47.22 485.16,-39.68 485.16,-39.68"/><text text-anchor="start" x="513.88" y="-113.3" font-family="Lato" font-size="14.00">a &amp; !b &amp; !c</text></g><!-- 3 --><g id="node6" class="node"><title>3</title><ellipse fill="#ffffaa" stroke="black" cx="102.88" cy="-117" rx="18" ry="18"/><ellipse fill="none" stroke="black" cx="102.88" cy="-117" rx="22" ry="22"/><text text-anchor="middle" x="102.88" y="-113.3" font-family="Lato" font-size="14.00">3</text></g><!-- 6&#45;&gt;3 --><g id="edge17" class="edge"><title>6&#45;&gt;3</title><path fill="none" stroke="black" d="M262.8,-205.63C240.04,-199.36 203.12,-187.8 173.88,-172 156,-162.34 137.79,-148.39 124.29,-137.09"/><polygon fill="black" stroke="black" points="118.81,-132.43 126.18,-134.56 121.48,-134.69 124.14,-136.96 124.14,-136.96 124.14,-136.96 121.48,-134.69 122.1,-139.36 118.81,-132.43 118.81,-132.43"/><text text-anchor="start" x="173.88" y="-160.8" font-family="Lato" font-size="14.00">!a &amp; b &amp; c</text></g><!-- 4 --><g id="node7" class="node"><title>4</title><ellipse fill="#ffffaa" stroke="black" cx="214.88" cy="-117" rx="18" ry="18"/><ellipse fill="none" stroke="black" cx="214.88" cy="-117" rx="22" ry="22"/><text text-anchor="middle" x="214.88" y="-113.3" font-family="Lato" font-size="14.00">4</text></g><!-- 6&#45;&gt;4 --><g id="edge18" class="edge"><title>6&#45;&gt;4</title><path fill="none" stroke="black" d="M268.43,-195.68C261.77,-188.73 254.1,-180.23 247.88,-172 241,-162.88 234.26,-152.26 228.69,-142.86"/><polygon fill="black" stroke="black" points="225.03,-136.58 231.27,-141.05 226.79,-139.61 228.55,-142.63 228.55,-142.63 228.55,-142.63 226.79,-139.61 225.83,-144.22 225.03,-136.58 225.03,-136.58"/><text text-anchor="start" x="247.88" y="-160.8" font-family="Lato" font-size="14.00">a &amp; !b &amp; c</text></g><!-- 5 --><g id="node8" class="node"><title>5</title><ellipse fill="#ffffaa" stroke="black" cx="425.88" cy="-117" rx="18" ry="18"/><ellipse fill="none" stroke="black" cx="425.88" cy="-117" rx="22" ry="22"/><text text-anchor="middle" x="425.88" y="-113.3" font-family="Lato" font-size="14.00">5</text></g><!-- 6&#45;&gt;5 --><g id="edge19" class="edge"><title>6&#45;&gt;5</title><path fill="none" stroke="black" d="M301.87,-199.22C327.12,-182.68 373.17,-152.52 401.49,-133.98"/><polygon fill="black" stroke="black" points="407.6,-129.98 403.47,-136.45 404.67,-131.89 401.74,-133.81 401.74,-133.81 401.74,-133.81 404.67,-131.89 400.02,-131.18 407.6,-129.98 407.6,-129.98"/><text text-anchor="start" x="362.88" y="-160.8" font-family="Lato" font-size="14.00">a &amp; b &amp; !c</text></g><!-- 0&#45;&gt;0 --><g id="edge2" class="edge"><title>0&#45;&gt;0</title><path fill="none" stroke="black" d="M117.46,-30.37C127.73,-31.53 136.88,-28.74 136.88,-22 136.88,-16.95 131.73,-14.11 124.83,-13.5"/><polygon fill="black" stroke="black" points="117.46,-13.63 124.41,-10.36 120.96,-13.57 124.46,-13.51 124.46,-13.51 124.46,-13.51 120.96,-13.57 124.52,-16.66 117.46,-13.63 117.46,-13.63"/><text text-anchor="start" x="136.88" y="-18.3" font-family="Lato" font-size="14.00">c</text></g><!-- 1&#45;&gt;1 --><g id="edge3" class="edge"><title>1&#45;&gt;1</title><path fill="none" stroke="black" d="M342.46,-30.37C352.73,-31.53 361.88,-28.74 361.88,-22 361.88,-16.95 356.73,-14.11 349.83,-13.5"/><polygon fill="black" stroke="black" points="342.46,-13.63 349.41,-10.36 345.96,-13.57 349.46,-13.51 349.46,-13.51 349.46,-13.51 345.96,-13.57 349.52,-16.66 342.46,-13.63 342.46,-13.63"/><text text-anchor="start" x="361.88" y="-18.3" font-family="Lato" font-size="14.00">b</text></g><!-- 2&#45;&gt;2 --><g id="edge4" class="edge"><title>2&#45;&gt;2</title><path fill="none" stroke="black" d="M492.46,-30.37C502.73,-31.53 511.88,-28.74 511.88,-22 511.88,-16.95 506.73,-14.11 499.83,-13.5"/><polygon fill="black" stroke="black" points="492.46,-13.63 499.41,-10.36 495.96,-13.57 499.46,-13.51 499.46,-13.51 499.46,-13.51 495.96,-13.57 499.52,-16.66 492.46,-13.63 492.46,-13.63"/><text text-anchor="start" x="511.88" y="-18.3" font-family="Lato" font-size="14.00">a</text></g><!-- 3&#45;&gt;0 --><g id="edge5" class="edge"><title>3&#45;&gt;0</title><path fill="none" stroke="black" d="M99.76,-94.99C99.02,-89.18 98.31,-82.85 97.88,-77 97.27,-68.61 96.96,-59.47 96.82,-51.13"/><polygon fill="black" stroke="black" points="96.74,-44.05 99.97,-51.02 96.78,-47.55 96.82,-51.05 96.82,-51.05 96.82,-51.05 96.78,-47.55 93.67,-51.09 96.74,-44.05 96.74,-44.05"/><text text-anchor="start" x="97.88" y="-65.8" font-family="Lato" font-size="14.00">!b &amp; 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c</text></g><!-- 4&#45;&gt;0 --><g id="edge8" class="edge"><title>4&#45;&gt;0</title><path fill="none" stroke="black" d="M210.61,-95.34C207.38,-84.24 201.91,-71.01 192.88,-62 174.59,-43.72 146.57,-33.68 125.52,-28.38"/><polygon fill="black" stroke="black" points="118.67,-26.76 126.21,-25.3 122.07,-27.56 125.48,-28.37 125.48,-28.37 125.48,-28.37 122.07,-27.56 124.76,-31.43 118.67,-26.76 118.67,-26.76"/><text text-anchor="start" x="202.88" y="-65.8" font-family="Lato" font-size="14.00">!a &amp; c</text></g><!-- 4&#45;&gt;2 --><g id="edge9" class="edge"><title>4&#45;&gt;2</title><path fill="none" stroke="black" d="M235.16,-107.56C261.77,-96.58 310.02,-77.04 351.88,-62 383.22,-50.74 419.65,-39.11 444.07,-31.51"/><polygon fill="black" stroke="black" points="450.94,-29.38 445.19,-34.46 447.6,-30.42 444.25,-31.45 444.25,-31.45 444.25,-31.45 447.6,-30.42 443.32,-28.44 450.94,-29.38 450.94,-29.38"/><text text-anchor="start" x="351.88" y="-65.8" font-family="Lato" font-size="14.00">a &amp; !c</text></g><!-- 4&#45;&gt;4 --><g id="edge10" class="edge"><title>4&#45;&gt;4</title><path fill="none" stroke="black" d="M235.46,-125.37C245.73,-126.53 254.88,-123.74 254.88,-117 254.88,-111.95 249.73,-109.11 242.83,-108.5"/><polygon fill="black" stroke="black" points="235.46,-108.63 242.41,-105.36 238.96,-108.57 242.46,-108.51 242.46,-108.51 242.46,-108.51 238.96,-108.57 242.52,-111.66 235.46,-108.63 235.46,-108.63"/><text text-anchor="start" x="254.88" y="-113.3" font-family="Lato" font-size="14.00">a &amp; 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b</text></g></g></svg>)
<spot.jupyter.SVG object>
%% Cell type:markdown id: tags:
Here is how to build an unambiguous automaton:
%% Cell type:code id: tags:
``` python
spot.translate('GFa -> GFb', 'unambig')
```
%%%% Output: execute_result
![](data:image/svg+xml;utf8,<?xml version="1.0" encoding="UTF-8" standalone="no"?><!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN""http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd"><!-- Generated by graphviz version 2.43.0 (0)--><!-- Pages: 1 --><svg width="298pt" height="347pt"viewBox="0.00 0.00 298.00 347.00" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g id="graph0" class="graph" transform="scale(1.0 1.0) rotate(0) translate(4 343)"><polygon fill="white" stroke="transparent" points="-4,4 -4,-343 294,-343 294,4 -4,4"/><text text-anchor="start" x="124.5" y="-324.8" font-family="Lato" font-size="14.00">Inf(</text><text text-anchor="start" x="145.5" y="-324.8" font-family="Lato" font-size="14.00" fill="#1f78b4">⓿</text><text text-anchor="start" x="161.5" y="-324.8" font-family="Lato" font-size="14.00">)</text><text text-anchor="start" x="123.5" y="-310.8" font-family="Lato" font-size="14.00">[Büchi]</text><!-- I --><!-- 0 --><g id="node2" class="node"><title>0</title><ellipse fill="#ffffaa" stroke="black" cx="56" cy="-131" rx="18" ry="18"/><text text-anchor="middle" x="56" y="-127.3" font-family="Lato" font-size="14.00">0</text></g><!-- I&#45;&gt;0 --><g id="edge1" class="edge"><title>I&#45;&gt;0</title><path fill="none" stroke="black" d="M1.15,-131C2.79,-131 17.15,-131 30.63,-131"/><polygon fill="black" stroke="black" points="37.94,-131 30.94,-134.15 34.44,-131 30.94,-131 30.94,-131 30.94,-131 34.44,-131 30.94,-127.85 37.94,-131 37.94,-131"/></g><!-- 1 --><g id="node3" class="node"><title>1</title><ellipse fill="#ffffaa" stroke="black" cx="156" cy="-204" rx="18" ry="18"/><text text-anchor="middle" x="156" y="-200.3" font-family="Lato" font-size="14.00">1</text></g><!-- 0&#45;&gt;1 --><g id="edge2" class="edge"><title>0&#45;&gt;1</title><path fill="none" stroke="black" d="M68.54,-144.52C75.02,-151.67 83.5,-160.33 92,-167 104.83,-177.07 120.67,-186.36 133.25,-193.11"/><polygon fill="black" stroke="black" points="139.5,-196.4 131.84,-195.93 136.41,-194.77 133.31,-193.14 133.31,-193.14 133.31,-193.14 136.41,-194.77 134.78,-190.35 139.5,-196.4 139.5,-196.4"/><text text-anchor="middle" x="105" y="-186.8" font-family="Lato" font-size="14.00">1</text></g><!-- 2 --><g id="node4" class="node"><title>2</title><ellipse fill="#ffffaa" stroke="black" cx="156" cy="-66" rx="18" ry="18"/><text text-anchor="middle" x="156" y="-62.3" font-family="Lato" font-size="14.00">2</text></g><!-- 0&#45;&gt;2 --><g id="edge3" class="edge"><title>0&#45;&gt;2</title><path fill="none" stroke="black" d="M71.46,-121.41C88.11,-110.37 115.57,-92.15 134.44,-79.64"/><polygon fill="black" stroke="black" points="140.48,-75.63 136.39,-82.12 137.56,-77.56 134.65,-79.5 134.65,-79.5 134.65,-79.5 137.56,-77.56 132.91,-76.87 140.48,-75.63 140.48,-75.63"/><text text-anchor="start" x="92" y="-109.8" font-family="Lato" font-size="14.00">a | b</text></g><!-- 3 --><g id="node5" class="node"><title>3</title><ellipse fill="#ffffaa" stroke="black" cx="270" cy="-123" rx="18" ry="18"/><text text-anchor="middle" x="270" y="-119.3" font-family="Lato" font-size="14.00">3</text></g><!-- 0&#45;&gt;3 --><g id="edge4" class="edge"><title>0&#45;&gt;3</title><path fill="none" stroke="black" d="M73.99,-133.48C105.7,-137.64 175.94,-144.68 234,-135 238.14,-134.31 242.45,-133.19 246.57,-131.91"/><polygon fill="black" stroke="black" points="253.26,-129.63 247.64,-134.87 249.94,-130.76 246.63,-131.88 246.63,-131.88 246.63,-131.88 249.94,-130.76 245.62,-128.9 253.26,-129.63 253.26,-129.63"/><text text-anchor="start" x="136" y="-142.8" font-family="Lato" font-size="14.00">!a &amp; 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<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7f9f5d7d4930> >
<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7f37382c05a0> >
%% Cell type:markdown id: tags:
Compare with the standard translation:
%% Cell type:code id: tags:
``` python
spot.translate('GFa -> GFb')
```
%%%% Output: execute_result
![](data:image/svg+xml;utf8,<?xml version="1.0" encoding="UTF-8" standalone="no"?><!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN""http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd"><!-- Generated by graphviz version 2.43.0 (0)--><!-- Pages: 1 --><svg width="165pt" height="263pt"viewBox="0.00 0.00 165.00 263.00" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g id="graph0" class="graph" transform="scale(1.0 1.0) rotate(0) translate(4 259)"><polygon fill="white" stroke="transparent" points="-4,4 -4,-259 161,-259 161,4 -4,4"/><text text-anchor="start" x="58" y="-240.8" font-family="Lato" font-size="14.00">Inf(</text><text text-anchor="start" x="79" y="-240.8" font-family="Lato" font-size="14.00" fill="#1f78b4">⓿</text><text text-anchor="start" x="95" y="-240.8" font-family="Lato" font-size="14.00">)</text><text text-anchor="start" x="57" y="-226.8" font-family="Lato" font-size="14.00">[Büchi]</text><!-- I --><!-- 0 --><g id="node2" class="node"><title>0</title><ellipse fill="#ffffaa" stroke="black" cx="56" cy="-69" rx="18" ry="18"/><text text-anchor="middle" x="56" y="-65.3" font-family="Lato" font-size="14.00">0</text></g><!-- I&#45;&gt;0 --><g id="edge1" class="edge"><title>I&#45;&gt;0</title><path fill="none" stroke="black" d="M1.15,-69C2.79,-69 17.15,-69 30.63,-69"/><polygon fill="black" stroke="black" points="37.94,-69 30.94,-72.15 34.44,-69 30.94,-69 30.94,-69 30.94,-69 34.44,-69 30.94,-65.85 37.94,-69 37.94,-69"/></g><!-- 0&#45;&gt;0 --><g id="edge2" class="edge"><title>0&#45;&gt;0</title><path fill="none" stroke="black" d="M49.62,-86.04C48.32,-95.86 50.45,-105 56,-105 60.17,-105 62.4,-99.86 62.71,-93.14"/><polygon fill="black" stroke="black" points="62.38,-86.04 65.85,-92.88 62.54,-89.53 62.71,-93.03 62.71,-93.03 62.71,-93.03 62.54,-89.53 59.56,-93.18 62.38,-86.04 62.38,-86.04"/><text text-anchor="start" x="51.5" y="-108.8" font-family="Lato" font-size="14.00">1</text></g><!-- 1 --><g id="node3" class="node"><title>1</title><ellipse fill="#ffffaa" stroke="black" cx="139" cy="-120" rx="18" ry="18"/><text text-anchor="start" x="134.5" y="-116.3" font-family="Lato" font-size="14.00">1</text></g><!-- 0&#45;&gt;1 --><g id="edge3" class="edge"><title>0&#45;&gt;1</title><path fill="none" stroke="black" d="M71.86,-78.35C84.53,-86.33 102.9,-97.9 117.06,-106.82"/><polygon fill="black" stroke="black" points="123.24,-110.71 115.64,-109.64 120.28,-108.84 117.31,-106.98 117.31,-106.98 117.31,-106.98 120.28,-108.84 118.99,-104.31 123.24,-110.71 123.24,-110.71"/><text text-anchor="start" x="93.5" y="-100.8" font-family="Lato" font-size="14.00">b</text></g><!-- 2 --><g id="node4" class="node"><title>2</title><ellipse fill="#ffffaa" stroke="black" cx="139" cy="-18" rx="18" ry="18"/><text text-anchor="middle" x="139" y="-14.3" font-family="Lato" font-size="14.00">2</text></g><!-- 0&#45;&gt;2 --><g id="edge4" class="edge"><title>0&#45;&gt;2</title><path fill="none" stroke="black" d="M71.86,-59.65C84.53,-51.67 102.9,-40.1 117.06,-31.18"/><polygon fill="black" stroke="black" points="123.24,-27.29 118.99,-33.69 120.28,-29.16 117.31,-31.02 117.31,-31.02 117.31,-31.02 120.28,-29.16 115.64,-28.36 123.24,-27.29 123.24,-27.29"/><text text-anchor="start" x="92" y="-49.8" font-family="Lato" font-size="14.00">!a</text></g><!-- 1&#45;&gt;1 --><g id="edge5" class="edge"><title>1&#45;&gt;1</title><path fill="none" stroke="black" d="M135.4,-137.78C134.79,-147.31 135.99,-156 139,-156 141.21,-156 142.44,-151.32 142.7,-145.05"/><polygon fill="black" stroke="black" points="142.6,-137.78 145.85,-144.74 142.65,-141.28 142.7,-144.78 142.7,-144.78 142.7,-144.78 142.65,-141.28 139.55,-144.83 142.6,-137.78 142.6,-137.78"/><text text-anchor="start" x="133" y="-159.8" font-family="Lato" font-size="14.00">!b</text></g><!-- 1&#45;&gt;1 --><g id="edge6" class="edge"><title>1&#45;&gt;1</title><path fill="none" stroke="black" d="M133.15,-137.14C129.71,-154.58 131.66,-174 139,-174 145.37,-174 147.68,-159.4 145.94,-144.15"/><polygon fill="black" stroke="black" points="144.85,-137.14 149.04,-143.58 145.39,-140.6 145.92,-144.06 145.92,-144.06 145.92,-144.06 145.39,-140.6 142.81,-144.54 144.85,-137.14 144.85,-137.14"/><text text-anchor="start" x="135" y="-192.8" font-family="Lato" font-size="14.00">b</text><text text-anchor="start" x="131" y="-177.8" font-family="Lato" font-size="14.00" fill="#1f78b4">⓿</text></g><!-- 2&#45;&gt;2 --><g id="edge7" class="edge"><title>2&#45;&gt;2</title><path fill="none" stroke="black" d="M131.97,-34.66C130.41,-44.62 132.75,-54 139,-54 143.69,-54 146.18,-48.73 146.47,-41.89"/><polygon fill="black" stroke="black" points="146.03,-34.66 149.6,-41.46 146.24,-38.16 146.46,-41.65 146.46,-41.65 146.46,-41.65 146.24,-38.16 143.31,-41.84 146.03,-34.66 146.03,-34.66"/><text text-anchor="start" x="133.5" y="-72.8" font-family="Lato" font-size="14.00">!a</text><text text-anchor="start" x="131" y="-57.8" font-family="Lato" font-size="14.00" fill="#1f78b4">⓿</text></g></g></svg>)
<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7f9f5d7d4cc0> >
<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7f37382c0ab0> >
%% Cell type:markdown id: tags:
And here is the automaton above with state-based acceptance:
%% Cell type:code id: tags:
``` python
a = spot.translate('GFa -> GFb', 'sbacc')
a
```
%%%% Output: execute_result
![](data:image/svg+xml;utf8,<?xml version="1.0" encoding="UTF-8" standalone="no"?><!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN""http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd"><!-- Generated by graphviz version 2.43.0 (0)--><!-- Pages: 1 --><svg width="257pt" height="220pt"viewBox="0.00 0.00 257.00 219.80" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g id="graph0" class="graph" transform="scale(1.0 1.0) rotate(0) translate(4 215.8)"><polygon fill="white" stroke="transparent" points="-4,4 -4,-215.8 253,-215.8 253,4 -4,4"/><text text-anchor="start" x="103" y="-181.6" font-family="Lato" font-size="14.00">[Büchi]</text><!-- I --><!-- 0 --><g id="node2" class="node"><title>0</title><ellipse fill="#ffffaa" stroke="black" cx="56" cy="-69" rx="18" ry="18"/><text text-anchor="middle" x="56" y="-65.3" font-family="Lato" font-size="14.00">0</text></g><!-- I&#45;&gt;0 --><g id="edge1" class="edge"><title>I&#45;&gt;0</title><path fill="none" stroke="black" 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168.33,-101.49"/><polygon fill="black" stroke="black" points="161.64,-104.75 166.55,-98.86 164.78,-103.22 167.93,-101.69 167.93,-101.69 167.93,-101.69 164.78,-103.22 169.31,-104.52 161.64,-104.75 161.64,-104.75"/><text text-anchor="start" x="185" y="-101.8" font-family="Lato" font-size="14.00">b</text></g><!-- 3&#45;&gt;3 --><g id="edge9" class="edge"><title>3&#45;&gt;3</title><path fill="none" stroke="black" d="M223.62,-133.66C221.98,-143.62 224.44,-153 231,-153 235.92,-153 238.54,-147.73 238.84,-140.89"/><polygon fill="black" stroke="black" points="238.38,-133.66 241.97,-140.45 238.61,-137.16 238.83,-140.65 238.83,-140.65 238.83,-140.65 238.61,-137.16 235.69,-140.85 238.38,-133.66 238.38,-133.66"/><text text-anchor="start" x="225" y="-156.8" font-family="Lato" font-size="14.00">!b</text></g></g></svg>)
<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7f9f5d7d4990> >
<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7f37382df240> >
%% Cell type:markdown id: tags:
Some example of running the self-loopization algorithm on an automaton:
%% Cell type:code id: tags:
``` python
a.is_empty()
```
%%%% Output: execute_result
False
%% Cell type:markdown id: tags:
Reading from file (see `automaton-io.ipynb` for more examples).
%% Cell type:code id: tags:
``` python
%%file example1.aut
HOA: v1
States: 3
Start: 0
AP: 2 "a" "b"
acc-name: Buchi
Acceptance: 5 Inf(0)&Fin(1)&Fin(4) | Inf(2)&Inf(3) | Inf(1)
--BODY--
State: 0 {3}
[t] 0
[0] 1 {1}
[!0] 2 {0 4}
State: 1 {3}
[1] 0
[0&1] 1 {0}
[!0&1] 2 {2 4}
State: 2
[!1] 0
[0&!1] 1 {0}
[!0&!1] 2 {0 4}
--END--
```
%%%% Output: stream
Writing example1.aut
%% Cell type:code id: tags:
``` python
a = spot.automaton('example1.aut')
display(a)
display(spot.remove_fin(a))
display(a.postprocess('TGBA', 'complete'))
display(a.postprocess('BA'))
```
%%%% Output: display_data
![](data:image/svg+xml;utf8,<?xml version="1.0" encoding="UTF-8" standalone="no"?><!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN""http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd"><!-- Generated by graphviz version 2.43.0 (0)--><!-- Pages: 1 --><svg width="354pt" height="178pt"viewBox="0.00 0.00 354.00 177.79" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g id="graph0" class="graph" transform="scale(1.0 1.0) rotate(0) translate(4 173.79)"><polygon fill="white" stroke="transparent" points="-4,4 -4,-173.79 350,-173.79 350,4 -4,4"/><text text-anchor="start" x="8" y="-155.59" font-family="Lato" font-size="14.00">(Inf(</text><text text-anchor="start" x="33" y="-155.59" font-family="Lato" font-size="14.00" fill="#1f78b4">⓿</text><text text-anchor="start" x="49" y="-155.59" font-family="Lato" font-size="14.00">) &amp; Fin(</text><text text-anchor="start" x="93" y="-155.59" font-family="Lato" font-size="14.00" fill="#ff4da0">❶</text><text text-anchor="start" x="109" y="-155.59" font-family="Lato" font-size="14.00">) &amp; Fin(</text><text text-anchor="start" x="153" y="-155.59" font-family="Lato" font-size="14.00" fill="#33a02c">❹</text><text text-anchor="start" x="169" y="-155.59" font-family="Lato" font-size="14.00">)) | (Inf(</text><text text-anchor="start" x="212" y="-155.59" font-family="Lato" font-size="14.00" fill="#ff7f00">❷</text><text text-anchor="start" x="228" y="-155.59" font-family="Lato" font-size="14.00">)&amp;Inf(</text><text text-anchor="start" x="262" y="-155.59" font-family="Lato" font-size="14.00" fill="#6a3d9a">❸</text><text text-anchor="start" x="278" y="-155.59" font-family="Lato" font-size="14.00">)) | Inf(</text><text text-anchor="start" x="318" y="-155.59" font-family="Lato" font-size="14.00" fill="#ff4da0">❶</text><text text-anchor="start" x="334" y="-155.59" font-family="Lato" font-size="14.00">)</text><!-- I --><!-- 0 --><g id="node2" class="node"><title>0</title><ellipse fill="#ffffaa" stroke="black" cx="73" cy="-23.79" rx="18" ry="18"/><text text-anchor="middle" x="73" y="-20.09" font-family="Lato" font-size="14.00">0</text></g><!-- I&#45;&gt;0 --><g id="edge1" class="edge"><title>I&#45;&gt;0</title><path fill="none" stroke="black" d="M18.15,-23.79C19.79,-23.79 34.15,-23.79 47.63,-23.79"/><polygon fill="black" stroke="black" points="54.94,-23.79 47.94,-26.94 51.44,-23.79 47.94,-23.79 47.94,-23.79 47.94,-23.79 51.44,-23.79 47.94,-20.64 54.94,-23.79 54.94,-23.79"/></g><!-- 0&#45;&gt;0 --><g id="edge2" class="edge"><title>0&#45;&gt;0</title><path fill="none" stroke="black" d="M66.62,-40.82C65.32,-50.65 67.45,-59.79 73,-59.79 77.17,-59.79 79.4,-54.65 79.71,-47.93"/><polygon fill="black" stroke="black" points="79.38,-40.82 82.85,-47.67 79.54,-44.32 79.71,-47.82 79.71,-47.82 79.71,-47.82 79.54,-44.32 76.56,-47.96 79.38,-40.82 79.38,-40.82"/><text text-anchor="start" x="68.5" y="-78.59" font-family="Lato" font-size="14.00">1</text><text text-anchor="start" x="65" y="-63.59" font-family="Lato" font-size="14.00" fill="#6a3d9a">❸</text></g><!-- 1 --><g id="node3" class="node"><title>1</title><ellipse fill="#ffffaa" stroke="black" cx="183" cy="-82.79" rx="18" ry="18"/><text text-anchor="middle" x="183" y="-79.09" font-family="Lato" font-size="14.00">1</text></g><!-- 0&#45;&gt;1 --><g id="edge3" class="edge"><title>0&#45;&gt;1</title><path fill="none" stroke="black" d="M81.44,-39.81C87.34,-50.65 96.65,-64.3 109,-71.79 123.6,-80.64 142.77,-83.26 157.8,-83.73"/><polygon fill="black" stroke="black" points="164.81,-83.81 157.77,-86.88 161.31,-83.77 157.81,-83.73 157.81,-83.73 157.81,-83.73 161.31,-83.77 157.85,-80.58 164.81,-83.81 164.81,-83.81"/><text text-anchor="start" x="121.5" y="-99.59" font-family="Lato" font-size="14.00">a</text><text text-anchor="start" x="109" y="-85.59" font-family="Lato" font-size="14.00" fill="#ff4da0">❶</text><text text-anchor="start" x="125" y="-85.59" font-family="Lato" font-size="14.00" fill="#6a3d9a">❸</text></g><!-- 2 --><g id="node4" class="node"><title>2</title><ellipse fill="#ffffaa" stroke="black" cx="309" cy="-23.79" rx="18" ry="18"/><text text-anchor="middle" x="309" y="-20.09" font-family="Lato" font-size="14.00">2</text></g><!-- 0&#45;&gt;2 --><g id="edge4" class="edge"><title>0&#45;&gt;2</title><path fill="none" stroke="black" d="M91.04,-23.17C125.44,-22.03 205.65,-19.86 273,-21.79 276.47,-21.89 280.13,-22.04 283.72,-22.22"/><polygon fill="black" stroke="black" points="290.92,-22.62 283.76,-25.38 287.42,-22.42 283.93,-22.23 283.93,-22.23 283.93,-22.23 287.42,-22.42 284.1,-19.09 290.92,-22.62 290.92,-22.62"/><text text-anchor="start" x="177.5" y="-38.59" font-family="Lato" font-size="14.00">!a</text><text text-anchor="start" x="159" y="-24.59" font-family="Lato" font-size="14.00" fill="#1f78b4">⓿</text><text text-anchor="start" x="175" y="-24.59" font-family="Lato" font-size="14.00" fill="#6a3d9a">❸</text><text text-anchor="start" x="191" y="-24.59" font-family="Lato" font-size="14.00" fill="#33a02c">❹</text></g><!-- 1&#45;&gt;0 --><g id="edge5" class="edge"><title>1&#45;&gt;0</title><path fill="none" stroke="black" d="M172.29,-67.96C164.91,-57.9 153.85,-45.13 141,-37.79 128.03,-30.38 111.64,-26.87 98.32,-25.22"/><polygon fill="black" stroke="black" points="91.27,-24.48 98.56,-22.08 94.75,-24.84 98.23,-25.21 98.23,-25.21 98.23,-25.21 94.75,-24.84 97.9,-28.34 91.27,-24.48 91.27,-24.48"/><text text-anchor="start" x="121" y="-56.59" font-family="Lato" font-size="14.00">b</text><text text-anchor="start" x="117" y="-41.59" font-family="Lato" font-size="14.00" fill="#6a3d9a">❸</text></g><!-- 1&#45;&gt;1 --><g id="edge6" class="edge"><title>1&#45;&gt;1</title><path fill="none" stroke="black" d="M173.19,-97.95C170.21,-108.45 173.48,-118.79 183,-118.79 190.29,-118.79 193.91,-112.73 193.87,-105.18"/><polygon fill="black" stroke="black" points="192.81,-97.95 196.95,-104.42 193.32,-101.42 193.83,-104.88 193.83,-104.88 193.83,-104.88 193.32,-101.42 190.71,-105.34 192.81,-97.95 192.81,-97.95"/><text text-anchor="start" x="167" y="-136.59" font-family="Lato" font-size="14.00">a &amp; b</text><text text-anchor="start" x="167" y="-122.59" font-family="Lato" font-size="14.00" fill="#1f78b4">⓿</text><text text-anchor="start" x="183" y="-122.59" font-family="Lato" font-size="14.00" fill="#6a3d9a">❸</text></g><!-- 1&#45;&gt;2 --><g id="edge7" class="edge"><title>1&#45;&gt;2</title><path fill="none" stroke="black" d="M201.01,-84.52C219.92,-85.63 250.73,-84.89 273,-71.79 283.21,-65.78 291.3,-55.5 297.12,-46"/><polygon fill="black" stroke="black" points="300.62,-39.91 299.86,-47.55 298.87,-42.95 297.13,-45.98 297.13,-45.98 297.13,-45.98 298.87,-42.95 294.4,-44.41 300.62,-39.91 300.62,-39.91"/><text text-anchor="start" x="231" y="-101.59" font-family="Lato" font-size="14.00">!a &amp; b</text><text text-anchor="start" x="225" y="-87.59" font-family="Lato" font-size="14.00" fill="#ff7f00">❷</text><text text-anchor="start" x="241" y="-87.59" font-family="Lato" font-size="14.00" fill="#6a3d9a">❸</text><text text-anchor="start" x="257" y="-87.59" font-family="Lato" font-size="14.00" fill="#33a02c">❹</text></g><!-- 2&#45;&gt;0 --><g id="edge8" class="edge"><title>2&#45;&gt;0</title><path fill="none" stroke="black" d="M291.49,-18.37C264.04,-10.04 207.25,4.35 159,-1.79 137.7,-4.5 114.1,-10.89 97.19,-16.09"/><polygon fill="black" stroke="black" points="90.37,-18.23 96.11,-13.12 93.71,-17.18 97.05,-16.13 97.05,-16.13 97.05,-16.13 93.71,-17.18 97.99,-19.13 90.37,-18.23 90.37,-18.23"/><text text-anchor="start" x="177" y="-5.59" font-family="Lato" font-size="14.00">!b</text></g><!-- 2&#45;&gt;1 --><g id="edge9" class="edge"><title>2&#45;&gt;1</title><path fill="none" stroke="black" d="M290.73,-23.48C273.16,-23.89 245.65,-26.52 225,-37.79 214.35,-43.6 205,-53.26 197.93,-62.13"/><polygon fill="black" stroke="black" points="193.62,-67.81 195.35,-60.33 195.74,-65.02 197.86,-62.23 197.86,-62.23 197.86,-62.23 195.74,-65.02 200.37,-64.14 193.62,-67.81 193.62,-67.81"/><text text-anchor="start" x="231" y="-56.59" font-family="Lato" font-size="14.00">a &amp; !b</text><text text-anchor="start" x="241" y="-41.59" font-family="Lato" font-size="14.00" fill="#1f78b4">⓿</text></g><!-- 2&#45;&gt;2 --><g id="edge10" class="edge"><title>2&#45;&gt;2</title><path fill="none" stroke="black" d="M298.85,-38.95C295.77,-49.45 299.16,-59.79 309,-59.79 316.54,-59.79 320.29,-53.73 320.25,-46.18"/><polygon fill="black" stroke="black" points="319.15,-38.95 323.32,-45.4 319.68,-42.41 320.2,-45.87 320.2,-45.87 320.2,-45.87 319.68,-42.41 317.09,-46.35 319.15,-38.95 319.15,-38.95"/><text text-anchor="start" x="289" y="-77.59" font-family="Lato" font-size="14.00">!a &amp; !b</text><text text-anchor="start" x="293" y="-63.59" font-family="Lato" font-size="14.00" fill="#1f78b4">⓿</text><text text-anchor="start" x="309" y="-63.59" font-family="Lato" font-size="14.00" fill="#33a02c">❹</text></g></g></svg>)
%%%% Output: display_data
![](data:image/svg+xml;utf8,<?xml version="1.0" encoding="UTF-8" standalone="no"?><!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN""http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd"><!-- Generated by graphviz version 2.43.0 (0)--><!-- Pages: 1 --><svg width="482pt" height="315pt"viewBox="0.00 0.00 482.00 315.00" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g id="graph0" class="graph" transform="scale(1.0 1.0) rotate(0) translate(4 311)"><polygon fill="white" stroke="transparent" points="-4,4 -4,-311 478,-311 478,4 -4,4"/><text text-anchor="start" x="161.5" y="-292.8" font-family="Lato" font-size="14.00">Inf(</text><text text-anchor="start" x="182.5" y="-292.8" font-family="Lato" font-size="14.00" fill="#1f78b4">⓿</text><text text-anchor="start" x="198.5" y="-292.8" font-family="Lato" font-size="14.00">) | (Inf(</text><text text-anchor="start" x="238.5" y="-292.8" font-family="Lato" font-size="14.00" fill="#ff4da0">❶</text><text text-anchor="start" x="254.5" y="-292.8" font-family="Lato" font-size="14.00">)&amp;Inf(</text><text text-anchor="start" x="288.5" y="-292.8" font-family="Lato" font-size="14.00" fill="#ff7f00">❷</text><text text-anchor="start" x="304.5" y="-292.8" font-family="Lato" font-size="14.00">))</text><text text-anchor="start" x="203" y="-278.8" font-family="Lato" font-size="14.00">[Fin&#45;less 3]</text><!-- I --><!-- 0 --><g id="node2" class="node"><title>0</title><ellipse fill="#ffffaa" stroke="black" cx="56" cy="-97" rx="18" ry="18"/><text text-anchor="middle" x="56" y="-93.3" font-family="Lato" font-size="14.00">0</text></g><!-- I&#45;&gt;0 --><g id="edge1" class="edge"><title>I&#45;&gt;0</title><path fill="none" stroke="black" d="M1.15,-97C2.79,-97 17.15,-97 30.63,-97"/><polygon fill="black" stroke="black" points="37.94,-97 30.94,-100.15 34.44,-97 30.94,-97 30.94,-97 30.94,-97 34.44,-97 30.94,-93.85 37.94,-97 37.94,-97"/></g><!-- 0&#45;&gt;0 --><g id="edge2" class="edge"><title>0&#45;&gt;0</title><path fill="none" stroke="black" d="M49.62,-114.04C48.32,-123.86 50.45,-133 56,-133 60.17,-133 62.4,-127.86 62.71,-121.14"/><polygon fill="black" stroke="black" points="62.38,-114.04 65.85,-120.88 62.54,-117.53 62.71,-121.03 62.71,-121.03 62.71,-121.03 62.54,-117.53 59.56,-121.18 62.38,-114.04 62.38,-114.04"/><text text-anchor="start" x="51.5" y="-151.8" font-family="Lato" font-size="14.00">1</text><text text-anchor="start" x="48" y="-136.8" font-family="Lato" font-size="14.00" fill="#ff7f00">❷</text></g><!-- 1 --><g id="node3" class="node"><title>1</title><ellipse fill="#ffffaa" stroke="black" cx="160" cy="-174" rx="18" ry="18"/><text text-anchor="middle" x="160" y="-170.3" font-family="Lato" font-size="14.00">1</text></g><!-- 0&#45;&gt;1 --><g id="edge3" class="edge"><title>0&#45;&gt;1</title><path fill="none" stroke="black" d="M73.27,-103C87.57,-108.77 108.46,-118.47 124,-131 131.88,-137.36 139.2,-145.75 145.08,-153.43"/><polygon fill="black" stroke="black" points="149.28,-159.12 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%%%% Output: display_data
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b</text><text text-anchor="start" x="352" y="-71.43" font-family="Lato" font-size="14.00" fill="#1f78b4">⓿</text></g><!-- 3&#45;&gt;4 --><g id="edge16" class="edge"><title>3&#45;&gt;4</title><path fill="none" stroke="black" d="M378.17,-31.63C395.18,-31.63 421.4,-31.63 440.57,-31.63"/><polygon fill="black" stroke="black" points="447.8,-31.63 440.8,-34.78 444.3,-31.63 440.8,-31.63 440.8,-31.63 440.8,-31.63 444.3,-31.63 440.8,-28.48 447.8,-31.63 447.8,-31.63"/><text text-anchor="start" x="396" y="-35.43" font-family="Lato" font-size="14.00">!a | !b</text></g><!-- 4&#45;&gt;4 --><g id="edge17" class="edge"><title>4&#45;&gt;4</title><path fill="none" stroke="black" d="M457.02,-47.55C454.68,-57.78 457.67,-67.63 466,-67.63 472.38,-67.63 475.63,-61.86 475.75,-54.56"/><polygon fill="black" stroke="black" points="474.98,-47.55 478.87,-54.17 475.36,-51.03 475.74,-54.51 475.74,-54.51 475.74,-54.51 475.36,-51.03 472.61,-54.85 474.98,-47.55 474.98,-47.55"/><text text-anchor="start" x="461.5" y="-71.43" font-family="Lato" font-size="14.00">1</text></g></g></svg>)
%%%% Output: display_data
![](data:image/svg+xml;utf8,<?xml version="1.0" encoding="UTF-8" standalone="no"?><!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN""http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd"><!-- Generated by graphviz version 2.43.0 (0)--><!-- Pages: 1 --><svg width="506pt" height="203pt"viewBox="0.00 0.00 506.00 202.80" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g id="graph0" class="graph" transform="scale(1.0 1.0) rotate(0) translate(4 198.8)"><polygon fill="white" stroke="transparent" points="-4,4 -4,-198.8 502,-198.8 502,4 -4,4"/><text text-anchor="start" x="227.5" y="-164.6" font-family="Lato" font-size="14.00">[Büchi]</text><!-- I --><!-- 0 --><g id="node2" class="node"><title>0</title><ellipse fill="#ffffaa" stroke="black" cx="56" cy="-18" rx="18" ry="18"/><text text-anchor="middle" x="56" y="-14.3" font-family="Lato" font-size="14.00">0</text></g><!-- I&#45;&gt;0 --><g id="edge1" class="edge"><title>I&#45;&gt;0</title><path fill="none" stroke="black" d="M1.15,-18C2.79,-18 17.15,-18 30.63,-18"/><polygon fill="black" stroke="black" points="37.94,-18 30.94,-21.15 34.44,-18 30.94,-18 30.94,-18 30.94,-18 34.44,-18 30.94,-14.85 37.94,-18 37.94,-18"/></g><!-- 0&#45;&gt;0 --><g id="edge2" class="edge"><title>0&#45;&gt;0</title><path fill="none" stroke="black" d="M49.62,-35.04C48.32,-44.86 50.45,-54 56,-54 60.17,-54 62.4,-48.86 62.71,-42.14"/><polygon fill="black" stroke="black" points="62.38,-35.04 65.85,-41.88 62.54,-38.53 62.71,-42.03 62.71,-42.03 62.71,-42.03 62.54,-38.53 59.56,-42.18 62.38,-35.04 62.38,-35.04"/><text text-anchor="start" x="51.5" y="-57.8" font-family="Lato" font-size="14.00">1</text></g><!-- 1 --><g id="node3" class="node"><title>1</title><ellipse fill="#ffffaa" stroke="black" cx="140" cy="-56" rx="18" ry="18"/><ellipse fill="none" stroke="black" cx="140" cy="-56" rx="22" ry="22"/><text text-anchor="start" x="135.5" y="-52.3" font-family="Lato" font-size="14.00">1</text></g><!-- 0&#45;&gt;1 --><g id="edge3" class="edge"><title>0&#45;&gt;1</title><path fill="none" stroke="black" d="M72.81,-25.33C84.22,-30.62 99.89,-37.88 113.12,-44.01"/><polygon fill="black" stroke="black" points="119.77,-47.09 112.1,-47.01 116.6,-45.62 113.42,-44.15 113.42,-44.15 113.42,-44.15 116.6,-45.62 114.75,-41.29 119.77,-47.09 119.77,-47.09"/><text text-anchor="start" x="92.5" y="-40.8" font-family="Lato" font-size="14.00">a</text></g><!-- 1&#45;&gt;0 --><g id="edge4" class="edge"><title>1&#45;&gt;0</title><path fill="none" stroke="black" d="M127.18,-37.94C120.39,-29.26 111.01,-19.72 100,-15 94.07,-12.46 87.25,-11.97 80.82,-12.44"/><polygon fill="black" stroke="black" points="73.53,-13.36 80.07,-9.36 77,-12.92 80.47,-12.48 80.47,-12.48 80.47,-12.48 77,-12.92 80.87,-15.61 73.53,-13.36 73.53,-13.36"/><text text-anchor="start" x="92" y="-18.8" font-family="Lato" font-size="14.00">b</text></g><!-- 2 --><g id="node4" class="node"><title>2</title><ellipse fill="#ffffaa" stroke="black" cx="248" cy="-69" rx="18" ry="18"/><text text-anchor="middle" x="248" y="-65.3" font-family="Lato" font-size="14.00">2</text></g><!-- 1&#45;&gt;2 --><g id="edge5" class="edge"><title>1&#45;&gt;2</title><path fill="none" stroke="black" d="M161.94,-58.57C179.36,-60.71 204.19,-63.75 222.52,-66"/><polygon fill="black" stroke="black" points="229.95,-66.91 222.61,-69.18 226.47,-66.48 223,-66.06 223,-66.06 223,-66.06 226.47,-66.48 223.38,-62.93 229.95,-66.91 229.95,-66.91"/><text text-anchor="start" x="180" y="-67.8" font-family="Lato" font-size="14.00">a &amp; b</text></g><!-- 3 --><g id="node5" class="node"><title>3</title><ellipse fill="#ffffaa" stroke="black" cx="360" cy="-51" rx="18" ry="18"/><ellipse fill="none" stroke="black" cx="360" cy="-51" rx="22" ry="22"/><text text-anchor="middle" x="360" y="-47.3" font-family="Lato" font-size="14.00">3</text></g><!-- 1&#45;&gt;3 --><g id="edge6" class="edge"><title>1&#45;&gt;3</title><path fill="none" stroke="black" d="M160.7,-47.59C178.45,-40.5 205.44,-30.9 230,-27 265.58,-21.35 306.42,-31.84 332.45,-40.68"/><polygon fill="black" stroke="black" points="339.39,-43.12 331.74,-43.77 336.08,-41.96 332.78,-40.8 332.78,-40.8 332.78,-40.8 336.08,-41.96 333.83,-37.83 339.39,-43.12 339.39,-43.12"/><text text-anchor="start" x="230" y="-30.8" font-family="Lato" font-size="14.00">!a &amp; b</text></g><!-- 4 --><g id="node6" class="node"><title>4</title><ellipse fill="#ffffaa" stroke="black" cx="476" cy="-100" rx="18" ry="18"/><ellipse fill="none" stroke="black" cx="476" cy="-100" rx="22" ry="22"/><text text-anchor="middle" x="476" y="-96.3" font-family="Lato" font-size="14.00">4</text></g><!-- 1&#45;&gt;4 --><g id="edge7" class="edge"><title>1&#45;&gt;4</title><path fill="none" stroke="black" d="M154.68,-72.58C170.62,-90.45 198.76,-117.83 230,-129 305.95,-156.17 402.75,-127.67 448.62,-110.7"/><polygon fill="black" stroke="black" points="455.27,-108.19 449.83,-113.61 451.99,-109.43 448.72,-110.66 448.72,-110.66 448.72,-110.66 451.99,-109.43 447.61,-107.72 455.27,-108.19 455.27,-108.19"/><text text-anchor="start" x="286" y="-143.8" font-family="Lato" font-size="14.00">a &amp; b</text></g><!-- 2&#45;&gt;2 --><g id="edge8" class="edge"><title>2&#45;&gt;2</title><path fill="none" stroke="black" d="M239.02,-84.92C236.68,-95.15 239.67,-105 248,-105 254.38,-105 257.63,-99.23 257.75,-91.93"/><polygon fill="black" stroke="black" points="256.98,-84.92 260.87,-91.53 257.36,-88.4 257.74,-91.87 257.74,-91.87 257.74,-91.87 257.36,-88.4 254.61,-92.22 256.98,-84.92 256.98,-84.92"/><text text-anchor="start" x="232" y="-108.8" font-family="Lato" font-size="14.00">a &amp; b</text></g><!-- 2&#45;&gt;3 --><g id="edge9" class="edge"><title>2&#45;&gt;3</title><path fill="none" stroke="black" d="M266.13,-70.23C280.64,-70.86 301.9,-70.83 320,-67 324.42,-66.06 328.97,-64.65 333.34,-63.04"/><polygon fill="black" stroke="black" points="340,-60.4 334.65,-65.91 336.75,-61.69 333.49,-62.98 333.49,-62.98 333.49,-62.98 336.75,-61.69 332.33,-60.05 340,-60.4 340,-60.4"/><text text-anchor="start" x="284" y="-73.8" font-family="Lato" font-size="14.00">!a &amp; b</text></g><!-- 3&#45;&gt;0 --><g id="edge10" class="edge"><title>3&#45;&gt;0</title><path fill="none" stroke="black" d="M342.55,-36.96C335.95,-32.06 328.01,-27.04 320,-24 228.34,10.78 198.03,-9.31 100,-8 96.44,-7.95 95.52,-7.51 92,-8 88.09,-8.55 84,-9.42 80.06,-10.44"/><polygon fill="black" stroke="black" points="73.18,-12.36 79.07,-7.44 76.55,-11.42 79.92,-10.47 79.92,-10.47 79.92,-10.47 76.55,-11.42 80.77,-13.51 73.18,-12.36 73.18,-12.36"/><text text-anchor="start" x="190" y="-7.8" font-family="Lato" font-size="14.00">!b</text></g><!-- 3&#45;&gt;2 --><g id="edge11" class="edge"><title>3&#45;&gt;2</title><path fill="none" stroke="black" d="M338.24,-46.81C322.96,-44.52 301.83,-43.06 284,-48 278.84,-49.43 273.67,-51.85 268.95,-54.55"/><polygon fill="black" stroke="black" points="262.84,-58.33 267.13,-51.97 265.81,-56.49 268.79,-54.65 268.79,-54.65 268.79,-54.65 265.81,-56.49 270.45,-57.32 262.84,-58.33 262.84,-58.33"/><text text-anchor="start" x="284" y="-51.8" font-family="Lato" font-size="14.00">a &amp; !b</text></g><!-- 3&#45;&gt;4 --><g id="edge12" class="edge"><title>3&#45;&gt;4</title><path fill="none" stroke="black" d="M380.6,-59.42C399.44,-67.52 428.04,-79.82 448.83,-88.75"/><polygon fill="black" stroke="black" points="455.28,-91.52 447.6,-91.65 452.06,-90.14 448.85,-88.76 448.85,-88.76 448.85,-88.76 452.06,-90.14 450.09,-85.86 455.28,-91.52 455.28,-91.52"/><text text-anchor="start" x="400" y="-85.8" font-family="Lato" font-size="14.00">a &amp; !b</text></g><!-- 4&#45;&gt;4 --><g id="edge13" class="edge"><title>4&#45;&gt;4</title><path fill="none" stroke="black" d="M465.57,-119.76C463.8,-130.35 467.28,-140 476,-140 482.68,-140 486.28,-134.34 486.81,-126.94"/><polygon fill="black" stroke="black" points="486.43,-119.76 489.94,-126.58 486.61,-123.25 486.8,-126.75 486.8,-126.75 486.8,-126.75 486.61,-123.25 483.65,-126.91 486.43,-119.76 486.43,-119.76"/><text text-anchor="start" x="460" y="-143.8" font-family="Lato" font-size="14.00">a &amp; b</text></g></g></svg>)
%% Cell type:code id: tags:
``` python
!rm example1.aut
```
%% Cell type:code id: tags:
``` python
spot.complete(a)
```
%%%% Output: execute_result
![](data:image/svg+xml;utf8,<?xml version="1.0" encoding="UTF-8" standalone="no"?><!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN""http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd"><!-- Generated by graphviz version 2.43.0 (0)--><!-- Pages: 1 --><svg width="398pt" height="189pt"viewBox="0.00 0.00 398.00 189.02" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g id="graph0" class="graph" transform="scale(1.0 1.0) rotate(0) translate(4 185.02)"><polygon fill="white" stroke="transparent" points="-4,4 -4,-185.02 394,-185.02 394,4 -4,4"/><text text-anchor="start" x="30" y="-166.82" font-family="Lato" font-size="14.00">(Inf(</text><text text-anchor="start" x="55" y="-166.82" font-family="Lato" font-size="14.00" fill="#1f78b4">⓿</text><text text-anchor="start" x="71" y="-166.82" font-family="Lato" font-size="14.00">) &amp; Fin(</text><text text-anchor="start" x="115" y="-166.82" font-family="Lato" font-size="14.00" fill="#ff4da0">❶</text><text text-anchor="start" x="131" y="-166.82" font-family="Lato" font-size="14.00">) &amp; Fin(</text><text text-anchor="start" x="175" y="-166.82" font-family="Lato" font-size="14.00" fill="#33a02c">❹</text><text text-anchor="start" x="191" y="-166.82" font-family="Lato" font-size="14.00">)) | (Inf(</text><text text-anchor="start" x="234" y="-166.82" font-family="Lato" font-size="14.00" fill="#ff7f00">❷</text><text text-anchor="start" x="250" y="-166.82" font-family="Lato" font-size="14.00">)&amp;Inf(</text><text text-anchor="start" x="284" y="-166.82" font-family="Lato" font-size="14.00" fill="#6a3d9a">❸</text><text text-anchor="start" x="300" y="-166.82" font-family="Lato" font-size="14.00">)) | Inf(</text><text text-anchor="start" x="340" y="-166.82" font-family="Lato" font-size="14.00" fill="#ff4da0">❶</text><text text-anchor="start" x="356" y="-166.82" font-family="Lato" font-size="14.00">)</text><!-- I --><!-- 0 --><g id="node2" class="node"><title>0</title><ellipse fill="#ffffaa" stroke="black" cx="56" cy="-26.02" rx="18" ry="18"/><text text-anchor="middle" x="56" y="-22.32" font-family="Lato" font-size="14.00">0</text></g><!-- I&#45;&gt;0 --><g id="edge1" class="edge"><title>I&#45;&gt;0</title><path fill="none" stroke="black" d="M1.15,-26.02C2.79,-26.02 17.15,-26.02 30.63,-26.02"/><polygon fill="black" stroke="black" points="37.94,-26.02 30.94,-29.17 34.44,-26.02 30.94,-26.02 30.94,-26.02 30.94,-26.02 34.44,-26.02 30.94,-22.87 37.94,-26.02 37.94,-26.02"/></g><!-- 0&#45;&gt;0 --><g id="edge2" class="edge"><title>0&#45;&gt;0</title><path fill="none" stroke="black" d="M49.62,-43.05C48.32,-52.87 50.45,-62.02 56,-62.02 60.17,-62.02 62.4,-56.87 62.71,-50.16"/><polygon fill="black" stroke="black" points="62.38,-43.05 65.85,-49.9 62.54,-46.55 62.71,-50.04 62.71,-50.04 62.71,-50.04 62.54,-46.55 59.56,-50.19 62.38,-43.05 62.38,-43.05"/><text text-anchor="start" x="51.5" y="-80.82" font-family="Lato" font-size="14.00">1</text><text text-anchor="start" x="48" y="-65.82" font-family="Lato" 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<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7f9f5d7d4c00> >
<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7f37382df1b0> >
%% Cell type:code id: tags:
``` python
spot.complete(spot.translate('Ga'))
```
%%%% Output: execute_result
![](data:image/svg+xml;utf8,<?xml version="1.0" encoding="UTF-8" standalone="no"?><!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN""http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd"><!-- Generated by graphviz version 2.43.0 (0)--><!-- Pages: 1 --><svg width="173pt" height="125pt"viewBox="0.00 0.00 173.00 124.80" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g id="graph0" class="graph" transform="scale(1.0 1.0) rotate(0) translate(4 120.8)"><polygon fill="white" stroke="transparent" points="-4,4 -4,-120.8 169,-120.8 169,4 -4,4"/><text text-anchor="start" x="61" y="-86.6" font-family="Lato" font-size="14.00">[Büchi]</text><!-- I --><!-- 0 --><g id="node2" class="node"><title>0</title><ellipse fill="#ffffaa" stroke="black" cx="60" cy="-22" rx="18" ry="18"/><ellipse fill="none" stroke="black" cx="60" cy="-22" rx="22" ry="22"/><text text-anchor="middle" x="60" y="-18.3" font-family="Lato" font-size="14.00">0</text></g><!-- I&#45;&gt;0 --><g id="edge1" class="edge"><title>I&#45;&gt;0</title><path fill="none" stroke="black" d="M1.17,-22C2.84,-22 16.88,-22 30.71,-22"/><polygon fill="black" stroke="black" points="37.86,-22 30.86,-25.15 34.36,-22 30.86,-22 30.86,-22 30.86,-22 34.36,-22 30.86,-18.85 37.86,-22 37.86,-22"/></g><!-- 0&#45;&gt;0 --><g id="edge2" class="edge"><title>0&#45;&gt;0</title><path fill="none" stroke="black" d="M52.68,-42.99C51.78,-53.09 54.22,-62 60,-62 64.34,-62 66.79,-56.99 67.37,-50.22"/><polygon fill="black" stroke="black" points="67.32,-42.99 70.52,-49.97 67.34,-46.49 67.37,-49.99 67.37,-49.99 67.37,-49.99 67.34,-46.49 64.22,-50.01 67.32,-42.99 67.32,-42.99"/><text text-anchor="start" x="56.5" y="-65.8" font-family="Lato" font-size="14.00">a</text></g><!-- 1 --><g id="node3" class="node"><title>1</title><ellipse fill="#ffffaa" stroke="black" cx="147" cy="-22" rx="18" ry="18"/><text text-anchor="middle" x="147" y="-18.3" font-family="Lato" font-size="14.00">1</text></g><!-- 0&#45;&gt;1 --><g id="edge3" class="edge"><title>0&#45;&gt;1</title><path fill="none" stroke="black" d="M82.01,-22C94.09,-22 109.32,-22 121.89,-22"/><polygon fill="black" stroke="black" points="128.94,-22 121.94,-25.15 125.44,-22 121.94,-22 121.94,-22 121.94,-22 125.44,-22 121.94,-18.85 128.94,-22 128.94,-22"/><text text-anchor="start" x="100" y="-25.8" font-family="Lato" font-size="14.00">!a</text></g><!-- 1&#45;&gt;1 --><g id="edge4" class="edge"><title>1&#45;&gt;1</title><path fill="none" stroke="black" d="M139.97,-38.66C138.41,-48.62 140.75,-58 147,-58 151.69,-58 154.18,-52.73 154.47,-45.89"/><polygon fill="black" stroke="black" points="154.03,-38.66 157.6,-45.46 154.24,-42.16 154.46,-45.65 154.46,-45.65 154.46,-45.65 154.24,-42.16 151.31,-45.84 154.03,-38.66 154.03,-38.66"/><text text-anchor="middle" x="147" y="-61.8" font-family="Lato" font-size="14.00">1</text></g></g></svg>)
<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7f9f5d7e2f90> >
<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7f37382dfae0> >
%% Cell type:code id: tags:
``` python
spot.formula('(a W c) & FGa').is_syntactic_persistence()
```
%%%% Output: execute_result
True
%% Cell type:code id: tags:
``` python
# Using +1 in the display options is a convient way to shift the
# set numbers in the output, as an aid in reading the product.
a1 = spot.translate('GF(a <-> Xa)')
print(a1.prop_weak())
a2 = spot.translate('a U b & GFc')
display_inline(a1.show('.t'), a2.show('.t+1'))
# the product should display pairs of states, unless asked not to (using '1').
p = spot.product(a1, a2)
display_inline(p.show('.t'), p.show('.t1'), per_row=2)
```
%%%% Output: stream
no
%%%% Output: display_data
%%%% Output: display_data
%% Cell type:markdown id: tags:
Explicit determinization after translation:
%% Cell type:code id: tags:
``` python
a = spot.translate('FGa')
display(a)
display(a.is_deterministic())
```
%%%% Output: display_data
![](data:image/svg+xml;utf8,<?xml version="1.0" encoding="UTF-8" standalone="no"?><!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN""http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd"><!-- Generated by graphviz version 2.43.0 (0)--><!-- Pages: 1 --><svg width="169pt" height="125pt"viewBox="0.00 0.00 169.00 124.80" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g id="graph0" class="graph" transform="scale(1.0 1.0) rotate(0) translate(4 120.8)"><polygon fill="white" stroke="transparent" points="-4,4 -4,-120.8 165,-120.8 165,4 -4,4"/><text text-anchor="start" x="59" y="-86.6" font-family="Lato" font-size="14.00">[Büchi]</text><!-- I --><!-- 0 --><g id="node2" class="node"><title>0</title><ellipse fill="#ffffaa" stroke="black" cx="56" cy="-22" rx="18" ry="18"/><text text-anchor="middle" x="56" y="-18.3" font-family="Lato" font-size="14.00">0</text></g><!-- I&#45;&gt;0 --><g id="edge1" class="edge"><title>I&#45;&gt;0</title><path fill="none" stroke="black" d="M1.15,-22C2.79,-22 17.15,-22 30.63,-22"/><polygon fill="black" stroke="black" points="37.94,-22 30.94,-25.15 34.44,-22 30.94,-22 30.94,-22 30.94,-22 34.44,-22 30.94,-18.85 37.94,-22 37.94,-22"/></g><!-- 0&#45;&gt;0 --><g id="edge2" class="edge"><title>0&#45;&gt;0</title><path fill="none" stroke="black" d="M49.62,-39.04C48.32,-48.86 50.45,-58 56,-58 60.17,-58 62.4,-52.86 62.71,-46.14"/><polygon fill="black" stroke="black" points="62.38,-39.04 65.85,-45.88 62.54,-42.53 62.71,-46.03 62.71,-46.03 62.71,-46.03 62.54,-42.53 59.56,-46.18 62.38,-39.04 62.38,-39.04"/><text text-anchor="start" x="51.5" y="-61.8" font-family="Lato" font-size="14.00">1</text></g><!-- 1 --><g id="node3" class="node"><title>1</title><ellipse fill="#ffffaa" stroke="black" cx="139" cy="-22" rx="18" ry="18"/><ellipse fill="none" stroke="black" cx="139" cy="-22" rx="22" ry="22"/><text text-anchor="start" x="134.5" y="-18.3" font-family="Lato" font-size="14.00">1</text></g><!-- 0&#45;&gt;1 --><g id="edge3" class="edge"><title>0&#45;&gt;1</title><path fill="none" stroke="black" d="M74.18,-22C84.48,-22 97.85,-22 109.68,-22"/><polygon fill="black" stroke="black" points="116.81,-22 109.81,-25.15 113.31,-22 109.81,-22 109.81,-22 109.81,-22 113.31,-22 109.81,-18.85 116.81,-22 116.81,-22"/><text text-anchor="start" x="92" y="-25.8" font-family="Lato" font-size="14.00">a</text></g><!-- 1&#45;&gt;1 --><g id="edge4" class="edge"><title>1&#45;&gt;1</title><path fill="none" stroke="black" d="M131.32,-42.99C130.37,-53.09 132.93,-62 139,-62 143.55,-62 146.13,-56.99 146.74,-50.22"/><polygon fill="black" stroke="black" points="146.68,-42.99 149.88,-49.97 146.71,-46.49 146.73,-49.99 146.73,-49.99 146.73,-49.99 146.71,-46.49 143.58,-50.01 146.68,-42.99 146.68,-42.99"/><text text-anchor="start" x="135.5" y="-65.8" font-family="Lato" font-size="14.00">a</text></g></g></svg>)
%%%% Output: display_data
%% Cell type:code id: tags:
``` python
spot.tgba_determinize(a)
```
%%%% Output: execute_result
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<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7f9f5d7d4b70> >