# -*- coding: utf-8 -*-
#+TITLE: =autfilt=
#+DESCRIPTION: Spot command-line tool for filtering, transforming, and converting ω-automata.
#+INCLUDE: setup.org
#+HTML_LINK_UP: tools.html
#+PROPERTY: header-args:sh :results verbatim :exports both
The =autfilt= tool can filter, transform, and convert a stream of automata.
The tool operates a loop over 5 phases:
- input one automaton
- optionally pre-process the automaton
- optionally filter the automaton (i.e., decide whether to ignore the
automaton or continue with it)
- optionally post-process the automaton (to simply it or change its acceptance)
- output the automaton
The simplest way to use the tool is simply to use it for input and
output (i.e., format conversion) without any transformation and
filtering.
* Conversion between formats
=autfilt= can read automata written in the [[http://adl.github.io/hoaf/][Hanoi Omega Automata
Format]], as [[http://spinroot.com/spin/Man/never.html][Spin never claims]], using [[http://www.tcs.hut.fi/Software/lbtt/doc/html/Format-for-automata.html][LBTT's format]], or using
[[http://www.ltl2dstar.de/docs/ltl2dstar.html][=ltl2dstar='s format]]. Automata in those formats (even a mix of those
formats) can be concatenated in the same stream, =autfilt= will
process them in batch. (The only restriction is that inside a file an
automaton in LBTT's format may not follow an automaton in
=ltl2dstar='s format.)
By default the output uses the HOA format. This can be changed using
[[file:oaut.org][the common output options]] like =--spin=, =--lbtt=, =--dot=,
=--stats=...
#+BEGIN_SRC sh :results silent
cat >example.hoa < 0
: 0 [label="0"]
: 0 -> 0 [label="p0\n{0}"]
: 0 -> 0 [label="!p0"]
: }
The =--spin= option implicitly requires a degeneralization:
#+BEGIN_SRC sh
autfilt example.hoa --spin
#+END_SRC
#+RESULTS:
#+begin_example
never {
accept_init:
if
:: ((p0)) -> goto accept_init
:: ((!(p0))) -> goto T0_S2
fi;
T0_S2:
if
:: ((p0)) -> goto accept_init
:: ((!(p0))) -> goto T0_S2
fi;
}
#+end_example
Option =--lbtt= only works for Büchi or generalized Büchi acceptance.
#+BEGIN_SRC sh
autfilt example.hoa --lbtt
#+END_SRC
#+RESULTS:
: 1 1t
: 0 1
: 0 0 -1 p0
: 0 -1 ! p0
: -1
* Displaying statistics
One special output format of =autfilt= is the statistic output. For
instance the following command calls [[file:randaut.org][=randaut=]] to generate 10 random
automata, and pipe the result into =autfilt= to display various
statistics.
#+BEGIN_SRC sh
randaut -n 10 -A0..2 -Q10..20 -e0.05 2 |
autfilt --stats='%s states, %e edges, %a acc-sets, %c SCCs, det=%d'
#+END_SRC
#+RESULTS:
#+begin_example
16 states, 30 edges, 1 acc-sets, 3 SCCs, det=0
20 states, 42 edges, 2 acc-sets, 1 SCCs, det=0
15 states, 27 edges, 2 acc-sets, 1 SCCs, det=0
10 states, 17 edges, 1 acc-sets, 1 SCCs, det=1
13 states, 25 edges, 1 acc-sets, 1 SCCs, det=0
11 states, 18 edges, 0 acc-sets, 1 SCCs, det=0
19 states, 41 edges, 2 acc-sets, 1 SCCs, det=0
11 states, 18 edges, 0 acc-sets, 1 SCCs, det=0
12 states, 21 edges, 1 acc-sets, 5 SCCs, det=0
18 states, 37 edges, 1 acc-sets, 5 SCCs, det=0
#+end_example
The following =%= sequences are available:
#+BEGIN_SRC sh :exports results
ltl2tgba --help | sed -n '/ sequences:/,/^$/p' | sed '1d;$d'
#+END_SRC
#+RESULTS:
#+begin_example
%< the part of the line before the formula if it
comes from a column extracted from a CSV file
%> the part of the line after the formula if it comes
from a column extracted from a CSV file
%% a single %
%a number of acceptance sets
%c, %[LETTERS]c number of SCCs; you may filter the SCCs to count
using the following LETTERS, possibly
concatenated: (a) accepting, (r) rejecting, (c)
complete, (v) trivial, (t) terminal, (w) weak,
(iw) inherently weak. Use uppercase letters to
negate them.
%d 1 if the output is deterministic, 0 otherwise
%e number of reachable edges
%f the formula, in Spot's syntax
%F name of the input file
%g, %[LETTERS]g acceptance condition (in HOA syntax); add brackets
to print an acceptance name instead and LETTERS to
tweak the format: (0) no parameters, (a)
accentuated, (b) abbreviated, (d) style used in
dot output, (g) no generalized parameter, (l)
recognize Street-like and Rabin-like, (m) no main
parameter, (p) no parity parameter, (o) name
unknown acceptance as 'other', (s) shorthand for
'lo0'.
%h the automaton in HOA format on a single line (use
%[opt]h to specify additional options as in
--hoa=opt)
%L location in the input file
%m name of the automaton
%n number of nondeterministic states in output
%p 1 if the output is complete, 0 otherwise
%r wall-clock time elapsed in seconds (excluding
parsing)
%R, %[LETTERS]R CPU time (excluding parsing), in seconds; Add
LETTERS to restrict to(u) user time, (s) system
time, (p) parent process, or (c) children
processes.
%s number of reachable states
%t number of reachable transitions
%u, %[e]u number of states (or [e]dges) with universal
branching
%u, %[LETTER]u 1 if the automaton contains some universal
branching (or a number of [s]tates or [e]dges with
universal branching)
%w one word accepted by the output automaton
%x, %[LETTERS]x number of atomic propositions declared in the
automaton; add LETTERS to list atomic
propositions with (n) no quoting, (s) occasional
double-quotes with C-style escape, (d)
double-quotes with C-style escape, (c)
double-quotes with CSV-style escape, (p) between
parentheses, any extra non-alphanumeric character
will be used to separate propositions
#+end_example
When a letter is available both as uppercase and lowercase, the
uppercase version refer to the input automaton, while the lowercase
refer to the output automaton. Of course this distinction makes sense
only if =autfilt= was instructed to perform an operation on the input
automaton.
* Filtering automata
=autfilt= offers multiple options to filter automata based on
different characteristics of the automaton.
#+BEGIN_SRC sh :exports results
autfilt --help | sed -n '/Filtering options.*:/,/^$/p' | sed '1d;$d'
#+END_SRC
#+RESULTS:
#+begin_example
--acc-sccs=RANGE, --accepting-sccs=RANGE
keep automata whose number of non-trivial
accepting SCCs is in RANGE
--acc-sets=RANGE keep automata whose number of acceptance sets is
in RANGE
--accept-word=WORD keep automata that accept WORD
--acceptance-is=NAME|FORMULA
match automata with given acceptance condition
--ap=RANGE match automata with a number of (declared) atomic
propositions in RANGE
--are-isomorphic=FILENAME keep automata that are isomorphic to the
automaton in FILENAME
--edges=RANGE keep automata whose number of edges is in RANGE
--equivalent-to=FILENAME keep automata that are equivalent
(language-wise) to the automaton in FILENAME
--has-exist-branching keep automata that use existential branching
(i.e., make non-deterministic choices)
--has-univ-branching keep alternating automata that use universal
branching
--included-in=FILENAME keep automata whose languages are included in that
of the automaton from FILENAME
--inherently-weak-sccs=RANGE
keep automata whose number of accepting
inherently-weak SCCs is in RANGE. An accepting
SCC is inherently weak if it does not have a
rejecting cycle.
--intersect=FILENAME keep automata whose languages have an non-empty
intersection with the automaton from FILENAME
--is-alternating keep only automata using universal branching
--is-colored keep colored automata (i.e., exactly one
acceptance mark per transition or state)
--is-complete keep complete automata
--is-deterministic keep deterministic automata
--is-empty keep automata with an empty language
--is-inherently-weak keep only inherently weak automata
--is-semi-deterministic keep semi-deterministic automata
--is-stutter-invariant keep automata representing stutter-invariant
properties
--is-terminal keep only terminal automata
--is-unambiguous keep only unambiguous automata
--is-very-weak keep only very-weak automata
--is-weak keep only weak automata
--nondet-states=RANGE keep automata whose number of nondeterministic
states is in RANGE
-N, --nth=RANGE assuming input automata are numbered from 1, keep
only those in RANGE
--rej-sccs=RANGE, --rejecting-sccs=RANGE
keep automata whose number of non-trivial
rejecting SCCs is in RANGE
--reject-word=WORD keep automata that reject WORD
--sccs=RANGE keep automata whose number of SCCs is in RANGE
--states=RANGE keep automata whose number of states is in RANGE
--terminal-sccs=RANGE keep automata whose number of accepting terminal
SCCs is in RANGE. Terminal SCCs are weak and
complete.
--triv-sccs=RANGE, --trivial-sccs=RANGE
keep automata whose number of trivial SCCs is in
RANGE
--unused-ap=RANGE match automata with a number of declared, but
unused atomic propositions in RANGE
--used-ap=RANGE match automata with a number of used atomic
propositions in RANGE
-u, --unique do not output the same automaton twice (same in
the sense that they are isomorphic)
-v, --invert-match select non-matching automata
--weak-sccs=RANGE keep automata whose number of accepting weak SCCs
is in RANGE. In a weak SCC, all transitions
belong to the same acceptance sets.
#+end_example
For instance =--states=2..5 --acc-sets=3= will /keep/ only automata that
use 3 acceptance sets, and that have between 2 and 5 states.
Except for =--unique=, all these filters can be inverted using option
=-v=. Using =--states=2..5 --acc-sets=3 -v= will /drop/ all automata
that use 3 acceptance sets and that have between 2 and 5 states, and
keep the others.
* Simplifying automata and changing acceptance conditions
:PROPERTIES:
:header-args:sh: :results verbatim :exports results
:END:
The standard set of automata simplification routines (these are often
referred to as the "post-processing" routines, because these are the
procedures performed by [[file:ltl2tgba.org][=ltl2tgba=]] after translating a formula into a
TGBA) are available through the following options.
This set of options controls the desired type of output automaton:
#+BEGIN_SRC sh
autfilt --help | sed -n '/Output automaton type:/,/^$/p' | sed '1d;$d'
#+END_SRC
#+RESULTS:
#+begin_example
-B, --ba Büchi Automaton (with state-based acceptance)
--cobuchi, --coBuchi automaton with co-Büchi acceptance (will
recognize a superset of the input language if not
co-Büchi realizable)
-C, --complete output a complete automaton
-G, --generic any acceptance is allowed (default)
-M, --monitor Monitor (accepts all finite prefixes of the given
property)
-p, --colored-parity[=any|min|max|odd|even|min odd|min even|max odd|max
even] colored automaton with parity acceptance
-P, --parity[=any|min|max|odd|even|min odd|min even|max odd|max even]
automaton with parity acceptance
-S, --state-based-acceptance, --sbacc
define the acceptance using states
--tgba Transition-based Generalized Büchi Automaton
#+end_example
These options specify any simplification goal:
#+BEGIN_SRC sh
autfilt --help | sed -n '/Simplification goal:/,/^$/p' | sed '1d;$d'
#+END_SRC
#+RESULTS:
: -a, --any no preference, do not bother making it small or
: deterministic
: -D, --deterministic prefer deterministic automata (combine with
: --generic to be sure to obtain a deterministic
: automaton)
: --small prefer small automata
Finally, the following switches control the amount of effort applied
toward the desired goal:
#+BEGIN_SRC sh
autfilt --help | sed -n '/Simplification level:/,/^$/p' | sed '1d;$d'
#+END_SRC
#+RESULTS:
: --high all available optimizations (slow)
: --low minimal optimizations (fast)
: --medium moderate optimizations
By default, =--any --low= is used, which cause all simplifications to
be skipped. However if any goal is given, than the simplification level
defaults to =--high= (unless specified otherwise). If a simplification
level is given without specifying any goal, then the goal default to =--small=.
So if you want to reduce the size of the automaton, try =--small= and
if you want to try to make (or keep) it deterministic use
=--deterministic=.
Note that the =--deterministic= flag has two possible behaviors
depending on the constraints on the acceptance conditions:
- When =autfilt= is configured to work with generic acceptance (the
=--generic= option, which is the default) or parity acceptance
(using =--parity= or =--colored-parity=), then the =--deterministic=
flag will do whatever it takes to output a deterministic automaton,
and this includes changing the acceptance condition if needed (see
below).
- If options =--tgba= or =--ba= are used, the =--deterministic= option
is taken as a /preference/: =autfilt= will try to favor determinism
in the output, but it may not always succeed and may output
non-deterministic automata. Note that if =autfilt --deterministic
--tgba= fails to output a deterministic automaton, it does not
necessarily implies that a deterministic TGBA does not exist: it
just implies that =autfilt= could not find it.
** Determinization
Spot has basically two ways to determinize automata, and that it uses
when =--deterministic= is passed.
- Automata that express obligation properties (this can be decided),
can be *determinized and minimized* into weak Büchi automata, as
discussed by [[http://www.daxc.de/eth/paper/atva07.pdf][Dax at al. (ATVA'07)]].
- Büchi automata (preferably with transition-based acceptance) can be
determinized into parity automata using a Safra-like procedure close
to the one presented by [[http://www.romanredz.se/papers/FI2012.pdf][Redziejowski (Fund. Inform. 119)]], with a few
additional tricks. This procedure does not necessarily produce a
minimal automaton.
When =--deterministic= is used, the first of these two procedures is
attempted on any supplied automaton. (It's even attempted for
deterministic automata, because the minimization might reduce them.)
If that first procedure failed, and the input automaton is not
deterministic and =--generic= (the default for =autfilt=), =--parity=
or =--colorized-parity= is used, then the second procedure is used.
In this case, automata will be first converted to transition-based
Büchi automata if their acceptance condition is more complex.
The difference between =--parity= and =--colored-parity= parity is
that the latter requests all transitions (or all states when
state-based acceptance is used) to belong to exactly one acceptance
set.
* Transformations
The following transformations are available:
#+BEGIN_SRC sh :exports results
autfilt --help | sed -n '/Transformations:/,/^$/p' | sed '1d;$d'
#+END_SRC
#+RESULTS:
#+begin_example
--cleanup-acceptance remove unused acceptance sets from the automaton
--cnf-acceptance put the acceptance condition in Conjunctive Normal
Form
--complement complement each automaton (different strategies
are used)
--complement-acceptance complement the acceptance condition (without
touching the automaton)
--decompose-scc=t|w|s|N|aN, --decompose-strength=t|w|s|N|aN
extract the (t) terminal, (w) weak, or (s) strong
part of an automaton or (N) the subautomaton
leading to the Nth SCC, or (aN) to the Nth
accepting SCC (option can be combined with commas
to extract multiple parts)
--destut allow less stuttering
--dnf-acceptance put the acceptance condition in Disjunctive Normal
Form
--dualize dualize each automaton
--exclusive-ap=AP,AP,... if any of those APs occur in the automaton,
restrict all edges to ensure two of them may not
be true at the same time. Use this option
multiple times to declare independent groups of
exclusive propositions.
--generalized-rabin[=unique-inf|share-inf], --gra[=unique-inf|share-inf]
rewrite the acceptance condition as generalized
Rabin; the default "unique-inf" option uses the
generalized Rabin definition from the HOA format;
the "share-inf" option allows clauses to share Inf
sets, therefore reducing the number of sets
--generalized-streett[=unique-fin|share-fin], --gsa[=unique-fin|share-fin] rewrite the
acceptance condition as generalized Streett; the
"share-fin" option allows clauses to share Fin
sets, therefore reducing the number of sets; the
default "unique-fin" does not
--instut[=1|2] allow more stuttering (two possible algorithms)
--keep-states=NUM[,NUM...] only keep specified states. The first state
will be the new initial state. Implies
--remove-unreachable-states.
--mask-acc=NUM[,NUM...] remove all transitions in specified acceptance
sets
--merge-transitions merge transitions with same destination and
acceptance
--product=FILENAME, --product-and=FILENAME
build the product with the automaton in FILENAME
to intersect languages
--product-or=FILENAME build the product with the automaton in FILENAME
to sum languages
--randomize[=s|t] randomize states and transitions (specify 's' or
't' to randomize only states or transitions)
--remove-ap=AP[=0|=1][,AP...]
remove atomic propositions either by existential
quantification, or by assigning them 0 or 1
--remove-dead-states remove states that are unreachable, or that cannot
belong to an infinite path
--remove-fin rewrite the automaton without using Fin acceptance
--remove-unreachable-states
remove states that are unreachable from the
initial state
--remove-unused-ap remove declared atomic propositions that are not
used
--sat-minimize[=options] minimize the automaton using a SAT solver
(only works for deterministic automata). Supported
options are acc=STRING, states=N, max-states=N,
sat-incr=N, sat-incr-steps=N, sat-langmap,
sat-naive, colored, preproc=N. Spot uses by
default its PicoSAT distribution but an external
SATsolver can be set thanks to the SPOT_SATSOLVER
environment variable(see spot-x).
--separate-sets if both Inf(x) and Fin(x) appear in the acceptance
condition, replace Fin(x) by a new Fin(y) and
adjust the automaton
--simplify-acceptance simplify the acceptance condition by merging
identical acceptance sets and by simplifying some
terms containing complementary sets
--simplify-exclusive-ap if --exclusive-ap is used, assume those AP
groups are actually exclusive in the system to
simplify the expression of transition labels
(implies --merge-transitions)
--split-edges split edges into transitions labeled by
conjunctions of all atomic propositions, so they
can be read as letters
--streett-like convert to an automaton with Streett-like
acceptance. Works only with acceptance condition
in DNF
--strip-acceptance remove the acceptance condition and all acceptance
sets
--sum=FILENAME, --sum-or=FILENAME
build the sum with the automaton in FILENAME to
sum languages
--sum-and=FILENAME build the sum with the automaton in FILENAME to
intersect languages
#+end_example
* Decorations
Decorations work by coloring some states or edges in the automaton.
They are only useful when the automaton is output in Dot format (with
=--dot= or =-d=) or HOA v1.1 format (with =-H1.1= or =--hoa=1.1=).
#+BEGIN_SRC sh :exports results
autfilt --help | sed -n '/^ *Decorations.*:/,/^$/p' | sed '1d;$d'
#+END_SRC
#+RESULTS:
#+begin_example
--highlight-accepting-run[=NUM]
highlight one accepting run using color NUM
--highlight-languages highlight states that recognize identical
languages
--highlight-nondet[=NUM] highlight nondeterministic states and edges
with color NUM
--highlight-nondet-edges[=NUM]
highlight nondeterministic edges with color NUM
--highlight-nondet-states[=NUM]
highlight nondeterministic states with color NUM
--highlight-word=[NUM,]WORD
highlight one run matching WORD using color NUM
#+end_example
Color numbers are indices in some hard-coded color palette. It is the
same palette that is currently used to display colored acceptance
sets, but this might change in the future.
* Examples
** Acceptance transformations
:PROPERTIES:
:header-args:sh: :results verbatim :exports code
:END:
Here is an automaton with transition-based acceptance:
#+BEGIN_SRC sh :results silent
cat >aut-ex1.hoa<