Commit c9d8d41f authored by Thomas Medioni's avatar Thomas Medioni

implement dualize to complement automatons

* NEWS: Mention the implementation
* python/spot/impl.i: Add dualize() to python interface.
* spot/twaalgos/Makefile.am: Add dualize.cc,hh to the build
* spot/twaalgos/dualize.cc: Implement dualize() that takes an automaton
  and returns its dual
* spot/twaalgos/dualize.hh: Implement dualize()
* tests/Makefile.am: Add dualize tests to the test suite
* tests/python/dualize.py: Test cases for dualize
parent cc0e9a5e
......@@ -21,6 +21,8 @@ New in spot 2.3.2.dev (not yet released)
- twa objects have a new property: prop_complete(). This obviously
acts as a cache for the is_complete() function.
- spot::dualize() implements the dual of any alternating automaton.
Bug fixes:
- In "lenient" mode the parser would fail to recover from
......
......@@ -120,6 +120,7 @@
#include <spot/twaalgos/cleanacc.hh>
#include <spot/twaalgos/degen.hh>
#include <spot/twaalgos/dot.hh>
#include <spot/twaalgos/dualize.hh>
#include <spot/twaalgos/copy.hh>
#include <spot/twaalgos/complete.hh>
#include <spot/twaalgos/complement.hh>
......@@ -541,6 +542,7 @@ def state_is_accepting(self, src) -> "bool":
%include <spot/twaalgos/ltl2tgba_fm.hh>
%include <spot/twaalgos/compsusp.hh>
%include <spot/twaalgos/determinize.hh>
%include <spot/twaalgos/dualize.hh>
%include <spot/twaalgos/langmap.hh>
%include <spot/twaalgos/magic.hh>
%include <spot/twaalgos/minimize.hh>
......
......@@ -43,6 +43,7 @@ twaalgos_HEADERS = \
dot.hh \
dtbasat.hh \
dtwasat.hh \
dualize.hh \
emptiness.hh \
emptiness_stats.hh \
gv04.hh \
......@@ -102,6 +103,7 @@ libtwaalgos_la_SOURCES = \
dot.cc \
dtbasat.cc \
dtwasat.cc \
dualize.cc \
emptiness.cc \
gv04.cc \
hoa.cc \
......
// -*- coding: utf-8 -*-
// Copyright (C) 2017 Laboratoire de Recherche et Développement
// de l'Epita (LRDE).
//
// This file is part of Spot, a model checking library.
//
// Spot is free software; you can redistribute it and/or modify it
// under the terms of the GNU General Public License as published by
// the Free Software Foundation; either version 3 of the License, or
// (at your option) any later version.
//
// Spot is distributed in the hope that it will be useful, but WITHOUT
// ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
// or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public
// License for more details.
//
// You should have received a copy of the GNU General Public License
// along with this program. If not, see <http://www.gnu.org/licenses/>.
#include <spot/misc/minato.hh>
#include <spot/twa/twagraph.hh>
#include <spot/twaalgos/alternation.hh>
#include <spot/twaalgos/cleanacc.hh>
#include <spot/twaalgos/complete.hh>
#include <spot/twaalgos/dualize.hh>
#include <spot/twaalgos/isdet.hh>
namespace spot
{
namespace
{
class dualizer final
{
private:
// Input automaton
const const_twa_graph_ptr aut_;
// State id to bdd variable association
// [id] == bddtrue means the state will be accepting everything
// (true state) in the dual automaton.
// [id] == bddfalse means the state will be rejecting everything
// (sink) in the dual automaton, which can lead to the removal of
// the transitions going into that state and therefore to the removal
// of the state when applying purge_unreachable_states().
// When [id] != bddtrue/bddfalse, the value correspond to the state
// bdd variable.
std::vector<bdd> state_to_var_;
// bdd variable to state id association
std::map<int, unsigned> var_to_state_;
// Acceptance mark to bdd variable association
std::vector<int> mark_to_var_;
// bdd variable to acceptance mark association
std::map<int, unsigned> var_to_mark_;
// bdd representing all the state variables
bdd all_states_;
// bdd representing all the marks variables
bdd all_marks_;
// bdd representing states & marks variables
bdd all_vars_;
// Id of the true state sink. -1U if none.
unsigned true_state_;
// In case the acceptance condition is never unsatisfied, but the
// automaton is not complete, we do transform the acceptance condition
// to Büchi, and need to mark all the existing transitions with the
// proper mark, that will be stored in acc_. 0U if not used.
acc_cond::mark_t acc_;
// Whether aut_ has a state accepting all.
bool has_sink;
// Any sink state in the input automaton will become a true state in the
// output. Knowing those allows us to simplify some universal transitions.
// There could be more than one sink state in the input automaton, and in
// this case they will be squashed into a single true state in the output
// automaton.
void find_sink_states(acc_cond::mark_t& second)
{
// Loop over the states and search a state that has no outgoing
// transitions, or only self-loops labeled by the same non-accepting
// mark. A similar test is done in complete_here().
unsigned n = aut_->num_states();
for (unsigned i = 0; i < n; ++i)
{
bool sinkable = true;
bool first = true;
acc_cond::mark_t commonacc = second;
for (auto& t: aut_->out(i))
{
if (t.dst != i)
{
sinkable = false;
break;
}
if (first)
{
commonacc = t.acc;
first = false;
}
else if (t.acc != commonacc)
{
sinkable = false;
break;
}
}
if (sinkable && !aut_->acc().accepting(commonacc))
{
second = commonacc;
state_to_var_[i] = bddtrue;
true_state_ = i;
has_sink = true;
}
}
}
// Any true state in the input automaton will become a sink state in the
// output. Knowing those allow us to simplify some universal transitions.
// There could be more than one true state in the input automaton. All
// true states from the input automaton will be removed in the output
// and the transitions leading to those states will be removed as well.
void find_true_states()
{
// Loop over the states and search a state that has a self-loop on
// any letter (bddtrue), with an accepting mark.
unsigned n = aut_->num_states();
for (unsigned i = 0; i < n; ++i)
{
bool acc_all = false;
for (auto& t: aut_->out(i))
{
if (t.dst == i && t.cond == bddtrue
&& aut_->acc().accepting(t.acc))
{
acc_all = true;
break;
}
}
if (acc_all)
{
state_to_var_[i] = bddfalse;
has_sink = true;
}
}
}
void copy_edges(const twa_graph_ptr &res)
{
std::vector<unsigned> st;
unsigned n = aut_->num_states();
for (unsigned i = 0; i < n; ++i)
{
bdd delta = dualized_transition_function(i);
bdd ap = bdd_exist(bdd_support(delta), all_vars_);
bdd letters = bdd_exist(delta, all_vars_);
while (letters != bddfalse)
{
bdd oneletter = bdd_satoneset(letters, ap, bddtrue);
letters -= oneletter;
minato_isop isop(delta & oneletter);
bdd cube;
while ((cube = isop.next()) != bddfalse)
{
bdd cond = bdd_exist(cube, all_vars_);
bdd dest = bdd_existcomp(cube, all_vars_);
st.clear();
acc_cond::mark_t m = bdd_to_state(dest, st);
if (st.empty())
{
st.push_back(true_state_);
if (aut_->prop_state_acc())
m = aut_->state_acc_sets(i);
}
res->new_univ_edge(i, st.begin(), st.end(), cond, m);
}
}
}
}
// Handles the dualization of a universal initial transition.
// In theory the transition would be split into several existential
// initial transitions, but since spot does not allow multiple initial
// states, we rather use a trick: We add a new initial state, and then
// copy all exiting transitions from each of the state of the universal
// initial transition.
void univ_init(const twa_graph_ptr& res)
{
bdd comb = bddfalse;
outedge_combiner oe(res);
for (unsigned c : aut_->univ_dests(aut_->get_init_state_number()))
comb |= oe(c);
auto s = res->new_state();
res->set_init_state(s);
oe.new_dests(s, comb);
}
// Allocates the states and marks as variables into the bdd dictionary.
// Also adds the corresponding mapping, and sets all_states_, all_marks_,
// and all_vars_ to hold those variables as bdds.
void allocate_dict_vars(const twa_graph_ptr& res)
{
auto dict = aut_->get_dict();
unsigned numstates = aut_->num_states();
all_states_ = bddtrue;
for (unsigned i = 0; i < numstates; ++i)
{
int v = dict->register_anonymous_variables(1, this);
if (state_to_var_[i] != bddtrue)
state_to_var_[i] = bdd_ithvar(v);
var_to_state_[v] = i;
all_states_ &= bdd_ithvar(v);
}
unsigned numsets = res->num_sets();
all_marks_ = bddtrue;
for (unsigned i = 0; i < numsets; ++i)
{
int v = dict->register_anonymous_variables(1, this);
mark_to_var_.push_back(v);
var_to_mark_.emplace(v, i);
all_marks_ &= bdd_ithvar(v);
}
all_vars_ = all_states_ & all_marks_;
}
// Returns the dualized transition function of any input state as a bdd.
bdd dualized_transition_function(unsigned state_id)
{
if (state_to_var_[state_id] == bddtrue)
return bddfalse;
bdd res = bddtrue;
for (auto& e : aut_->out(state_id))
{
bdd dest = bddfalse;
for (unsigned d : aut_->univ_dests(e))
dest |= state_to_var_[d];
bdd mark_bdd = bddtrue;
acc_cond::mark_t m = acc_ ? acc_ : e.acc;
for (unsigned s: m.sets())
mark_bdd &= bdd_ithvar(mark_to_var_[s]);
res &= bdd_imp(e.cond, mark_bdd & dest);
}
return res;
}
// Given the bdd representation b of a transition, adds destination states
// to s, and returns the marks on the transition. s being empty means the
// transition goes toward a "forever true" state. s with size one
// represents an existential transition, while size over one represents
// a universal transition.
acc_cond::mark_t bdd_to_state(bdd b, std::vector<unsigned>& s)
{
acc_cond::mark_t m = 0U;
while (b != bddtrue)
{
assert(bdd_low(b) == bddfalse);
int v = bdd_var(b);
auto it = var_to_state_.find(v);
if (it != var_to_state_.end())
s.push_back(it->second);
else
m.set(var_to_mark_[v]);
b = bdd_high(b);
}
return m;
}
public:
dualizer(const const_twa_graph_ptr& aut)
: aut_(aut),
state_to_var_(aut_->num_states(), bddfalse),
true_state_(-1U),
acc_(0U),
has_sink(false)
{
}
~dualizer()
{
aut_->get_dict()->unregister_all_my_variables(this);
}
twa_graph_ptr run()
{
bool cmpl = is_complete(aut_);
auto um = aut_->acc().unsat_mark();
auto res = make_twa_graph(aut_->get_dict());
res->copy_ap_of(aut_);
if (!um.first && cmpl)
{
//Shortcut if dual is false
res->new_states(1);
res->new_edge(0, 0, bddtrue, 0U);
res->set_init_state(0);
res->set_acceptance(0, acc_cond::acc_code::f());
res->prop_terminal(true);
res->prop_complete(true);
res->prop_universal(true);
return res;
}
if (is_deterministic(aut_))
{
res = cleanup_acceptance_here(spot::complete(aut_));
res->set_acceptance(res->num_sets(),
res->get_acceptance().complement());
// Complementing the acceptance is likely to break the terminal
// property, but not weakness. We make a useless call to
// prop_keep() just so we remember to update it in the future if a
// new argument is added.
res->prop_keep({true, true, true, true, true, true});
res->prop_terminal(trival::maybe());
return res;
}
const_twa_graph_ptr autptr;
res->new_states(aut_->num_states());
if (!cmpl)
{
if (!um.first)
{
acc_ = res->set_buchi();
autptr = res;
}
else
{
find_sink_states(um.second);
autptr = aut_;
}
if (true_state_ == -1U)
true_state_ = res->new_state();
}
// This case does not cover cmpl && !um.first
// Due to previous test shortcutting automatons that accept all words.
else
{
assert(um.first);
find_sink_states(um.second);
autptr = aut_;
}
if (true_state_ != -1U)
res->new_edge(true_state_, true_state_, bddtrue, um.second);
res->set_acceptance(autptr->num_sets(),
autptr->get_acceptance().complement());
allocate_dict_vars(res);
find_true_states();
copy_edges(res);
unsigned init_state = aut_->get_init_state_number();
if (aut_->is_univ_dest(init_state))
univ_init(res);
else
res->set_init_state(init_state);
res->merge_edges();
res->purge_unreachable_states();
res->prop_copy(aut_, {true, true, false, false, false, true});
res->prop_terminal(trival::maybe());
if (!has_sink)
res->prop_complete(true);
cleanup_acceptance_here(res);
return res;
}
};
}
twa_graph_ptr dualize(const const_twa_graph_ptr& aut)
{
dualizer du(aut);
return du.run();
}
}
// -*- coding: utf-8 -*-
// Copyright (C) 2017 Laboratoire de Recherche et Développement de
// l'Epita (LRDE).
//
// This file is part of Spot, a model checking library.
//
// Spot is free software; you can redistribute it and/or modify it
// under the terms of the GNU General Public License as published by
// the Free Software Foundation; either version 3 of the License, or
// (at your option) any later version.
//
// Spot is distributed in the hope that it will be useful, but WITHOUT
// ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
// or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public
// License for more details.
//
// You should have received a copy of the GNU General Public License
// along with this program. If not, see <http://www.gnu.org/licenses/>.
#pragma once
#include <spot/misc/common.hh>
#include <spot/twa/fwd.hh>
namespace spot
{
/// \brief Complement an automaton by dualizing it.
///
/// Given an automaton \a aut of any type, produces the dual as output. The
/// automaton will be completed if it isn't already. If it is deterministic
/// and complete, complementing the automaton can be done by just
/// complementing the acceptance condition.
///
/// In particular, this implies that an input that use generalized Büchi will
/// be output as generalized co-Büchi.
///
/// Functions like to_generalized_buchi() or remove_fin() are frequently
/// called on existential automatons after dualize() to obtain an easier
/// acceptance condition, but maybe at the cost of losing determinism.
///
/// If the input automaton is deterministic, the output will be deterministic.
/// If the input automaton is existential, the output will be universal.
/// If the input automaton is universal, the output will be existential.
/// Finally, if the input automaton is alternating, the result is alternating.
/// More can be found on page 22 (Definition 1.6) of:
/** \verbatim
@mastersthesis{loding.98.methodsfor
author = {Christof Löding}
title = {Methods for the Transformation of ω-Automata: Complexity
and Connection to Second Order Logic}
school = {Institute of Computer Science and Applied Mathematics
Christian-Albrechts-University of Kiel}
year = {1998}
}
\endverbatim */
SPOT_API twa_graph_ptr
dualize(const const_twa_graph_ptr& aut);
}
......@@ -332,6 +332,7 @@ TESTS_python = \
python/bugdet.py \
python/declenv.py \
python/decompose_scc.py \
python/dualize.py \
python/implies.py \
python/interdep.py \
python/ltl2tgba.test \
......
#!/usr/bin/python3
# -*- mode: python; coding: utf-8 -*-
# Copyright (C) 2017 Laboratoire de Recherche et Développement de
# l'EPITA.
#
# This file is part of Spot, a model checking library.
#
# Spot is free software; you can redistribute it and/or modify it
# under the terms of the GNU General Public License as published by
# the Free Software Foundation; either version 3 of the License, or
# (at your option) any later version.
#
# Spot is distributed in the hope that it will be useful, but WITHOUT
# ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
# or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public
# License for more details.
#
# You should have received a copy of the GNU General Public License
# along with this program. If not, see <http://www.gnu.org/licenses/>.
import spot
import buddy
match_strings = [('is_buchi', 'is_co_buchi'),\
('is_generalized_buchi', 'is_generalized_co_buchi'),\
('is_all', 'is_none'),\
('is_all', 'is_all'),
('is_buchi', 'is_all')]
def dualtype(aut, dual):
if dual.acc().is_none(): return True
return (not spot.is_deterministic(aut) or spot.is_deterministic(dual))\
and (spot.is_universal(dual) or not aut.is_existential())\
and (dual.is_existential() or not spot.is_universal(aut))
def produce_phi(rg, n):
phi = []
while len(phi) < n:
phi.append(rg.next())
return phi
def produce_automaton(phi):
aut = []
for f in phi:
aut.append(spot.translate(f))
return aut
def test_aut(aut, d = None):
if d is None:
d = spot.dualize(aut)
aa = aut.acc()
da = d.acc()
complete = spot.is_complete(aut)
univ = aut.is_univ_dest(aut.get_init_state_number())
an = aut.num_states()
dn = d.num_states()
if not dualtype(aut, d):
return (False, 'Incorrect transition mode resulting of dual')
for p in match_strings:
if ((getattr(aa, p[0])() and getattr(da, p[1])())\
or (getattr(aa, p[1])() and getattr(da, p[0])())):
return (True, '')
return (False, 'Incorrect acceptance type dual')
def test_assert(a, d=None):
t = test_aut(a, d)
if not t[0]:
print (t[1])
print (a.to_str('hoa'))
print (spot.dualize(a).to_str('hoa'))
assert False
aut = spot.translate('a')
test_assert(aut)
dual = spot.dualize(aut)
h = dual.to_str('hoa')
assert h == """HOA: v1
States: 3
Start: 1
AP: 1 "a"
acc-name: co-Buchi
Acceptance: 1 Fin(0)
properties: trans-labels explicit-labels state-acc complete
properties: deterministic stutter-invariant weak
--BODY--
State: 0 {0}
[t] 0
State: 1
[0] 0
[!0] 2
State: 2
[t] 2
--END--"""
aut = spot.automaton("""
HOA: v1
States: 3
Start: 0
AP: 2 "a" "b"
acc-name: Buchi
Acceptance: 1 Inf(0)
properties: trans-labels explicit-labels state-acc
--BODY--
State: 0
[0] 1
[0] 2
State: 1 {0}
[0] 1
State: 2 {0}
[1] 2
--END--""")
test_assert(aut)
dual = spot.dualize(aut)
h = dual.to_str('hoa')
assert h == """HOA: v1
States: 4
Start: 0
AP: 2 "a" "b"
acc-name: co-Buchi
Acceptance: 1 Fin(0)
properties: univ-branch trans-labels explicit-labels state-acc complete
properties: deterministic
--BODY--
State: 0
[!0] 3
[0] 1&2
State: 1 {0}
[0] 1
[!0] 3
State: 2 {0}
[1] 2
[!1] 3
State: 3
[t] 3
--END--"""
aut = spot.automaton("""
HOA: v1
States: 4
Start: 0&2
AP: 2 "a" "b"
acc-name: Buchi
Acceptance: 1 Inf(0)
properties: trans-labels explicit-labels state-acc univ-branch
--BODY--
State: 0
[0] 1
State: 1 {0}
[t] 1
State: 2
[1] 3
<