spot/spot/twaalgos/remfin.cc
Alexandre Duret-Lutz 3dc084c4f6 use mask_keep_accessible_states
* bin/autfilt.cc, spot/twaalgos/isweakscc.cc, spot/twaalgos/remfin.cc,
spot/twaalgos/sccinfo.cc: Use mask_keep_accessible_states instead of
mask_keep_states.
2016-10-19 10:51:38 +02:00

758 lines
26 KiB
C++

// -*- coding: utf-8 -*-
// Copyright (C) 2015, 2016 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/>.
#include <spot/twaalgos/remfin.hh>
#include <spot/twaalgos/sccinfo.hh>
#include <iostream>
#include <spot/twaalgos/cleanacc.hh>
#include <spot/twaalgos/totgba.hh>
#include <spot/twaalgos/isdet.hh>
#include <spot/twaalgos/mask.hh>
//#define TRACE
#ifdef TRACE
#define trace std::cerr
#else
#define trace while (0) std::cerr
#endif
namespace spot
{
namespace
{
// Check whether the SCC composed of all states STATES, and
// visiting all acceptance marks in SETS contains non-accepting
// cycles.
//
// A cycle is accepting (in a Rabin automaton) if there exists an
// acceptance pair (Fᵢ, Iᵢ) such that some states from Iᵢ are
// visited while no states from Fᵢ are visited.
//
// Consequently, a cycle is non-accepting if for all acceptance
// pairs (Fᵢ, Iᵢ), either no states from Iᵢ are visited or some
// states from Fᵢ are visited. (This corresponds to an accepting
// cycle with Streett acceptance.)
static bool
is_scc_ba_type(const const_twa_graph_ptr& aut,
const std::vector<unsigned>& states,
std::vector<bool>& final,
acc_cond::mark_t inf_pairs,
acc_cond::mark_t inf_alone,
acc_cond::mark_t sets)
{
// Consider the SCC as one large cycle and check its
// intersection with all Fᵢs and Iᵢs: This is the SETS
// variable.
//
// Let f=[F₁,F₂,...] and i=[I₁,I₂,...] be bitvectors where bit
// Fᵢ (resp. Iᵢ) indicates that Fᵢ (resp. Iᵢ) has been visited
// in the SCC.
acc_cond::mark_t f = (sets << 1U) & inf_pairs;
acc_cond::mark_t i = sets & inf_pairs;
// If we have i&!f = [0,0,...] that means that the cycle formed
// by the entire SCC is not accepting. However that does not
// necessarily imply that all cycles in the SCC are also
// non-accepting. We may have a smaller cycle that is
// accepting, but which becomes non-accepting when extended with
// more states.
i -= f;
i |= (inf_alone & sets);
if (!i)
{
// Check whether the SCC is accepting. We do that by simply
// converting that SCC into a TGBA and running our emptiness
// check. This is not a really smart implementation and
// could be improved.
std::vector<bool> keep(aut->num_states(), false);
for (auto s: states)
keep[s] = true;
auto sccaut = mask_keep_accessible_states(aut, keep, states.front());
// Force SBA to false. It does not affect the emptiness
// check result, however it prevent recurring into this
// procedure, because empty() will call to_tgba() which will
// call remove_fin()...
sccaut->prop_state_acc(false);
// If SCCAUT is empty, the SCC is BA-type (and none
// of its states are final). If SCCAUT is nonempty, the SCC
// is not BA type.
return sccaut->is_empty();
}
// The bits remaining sets in i corresponds to I₁s that have
// been seen with seeing the mathing F₁. In this SCC any state
// in these I₁ is therefore final. Otherwise we do not know: it
// is possible that there is a non-accepting cycle in the SCC
// that do not visit Fᵢ.
std::set<unsigned> unknown;
for (auto s: states)
{
if (aut->state_acc_sets(s) & i)
final[s] = true;
else
unknown.insert(s);
}
// Check whether it is possible to build non-accepting cycles
// using only the "unknown" states.
while (!unknown.empty())
{
std::vector<bool> keep(aut->num_states(), false);
for (auto s: unknown)
keep[s] = true;
scc_info si(mask_keep_states(aut, keep, *unknown.begin()));
unsigned scc_max = si.scc_count();
for (unsigned scc = 0; scc < scc_max; ++scc)
{
for (auto s: si.states_of(scc))
unknown.erase(s);
if (si.is_rejecting_scc(scc)) // this includes trivial SCCs
continue;
if (!is_scc_ba_type(aut, si.states_of(scc),
final, inf_pairs, 0U, si.acc(scc)))
return false;
}
}
return true;
}
// Specialized conversion from Rabin acceptance to Büchi acceptance.
// Is able to detect SCCs that are Büchi-type (i.e., they can be
// converted to Büchi acceptance without chaning their structure).
// Currently only works with state-based acceptance.
//
// See "Deterministic ω-automata vis-a-vis Deterministic Büchi
// Automata", S. Krishnan, A. Puri, and R. Brayton (ISAAC'94) for
// some details about detecting Büchi-typeness.
//
// We essentially apply this method SCC-wise. The paper is
// concerned about *deterministic* automata, but we apply the
// algorithm on non-deterministic automata as well: in the worst
// case it is possible that a Büchi-type SCC with some
// non-deterministic has one accepting and one rejecting run for
// the same word. In this case we may fail to detect the
// Büchi-typeness of the SCC, but the resulting automaton should
// be correct nonetheless.
static twa_graph_ptr
ra_to_ba(const const_twa_graph_ptr& aut,
acc_cond::mark_t inf_pairs,
acc_cond::mark_t inf_alone,
acc_cond::mark_t fin_alone)
{
assert((bool)aut->prop_state_acc());
scc_info si(aut);
// For state-based Rabin automata, we check each SCC for
// BA-typeness. If an SCC is BA-type, its final states are stored
// in BA_FINAL_STATES.
std::vector<bool> scc_is_ba_type(si.scc_count(), false);
bool ba_type = false;
std::vector<bool> ba_final_states;
#ifdef DEBUG
acc_cond::mark_t fin;
acc_cond::mark_t inf;
std::tie(inf, fin) = aut->get_acceptance().used_inf_fin_sets();
assert(inf == (inf_pairs | inf_alone));
assert(fin == ((inf_pairs >> 1U) | fin_alone));
#endif
ba_final_states.resize(aut->num_states(), false);
ba_type = true; // until proven otherwise
unsigned scc_max = si.scc_count();
for (unsigned scc = 0; scc < scc_max; ++scc)
{
if (si.is_rejecting_scc(scc)) // this includes trivial SCCs
{
scc_is_ba_type[scc] = true;
continue;
}
bool scc_ba_type = false;
auto sets = si.acc(scc);
// If there is one fin_alone that is not in the SCC,
// any cycle in the SCC is accepting. Mark all states
// as final.
if ((sets & fin_alone) != fin_alone)
{
for (auto s: si.states_of(scc))
ba_final_states[s] = true;
scc_ba_type = true;
}
// Conversely, if all fin_alone appear in the SCC, then it
// cannot be accepting.
else if (sets & fin_alone)
{
scc_ba_type = false;
}
// In the generale case (no fin_alone involved), we need
// a dedicated check.
else
{
scc_ba_type = is_scc_ba_type(aut, si.states_of(scc),
ba_final_states,
inf_pairs, inf_alone, si.acc(scc));
}
ba_type &= scc_ba_type;
scc_is_ba_type[scc] = scc_ba_type;
}
#ifdef TRACE
trace << "SCC DBA-realizibility\n";
for (unsigned scc = 0; scc < scc_max; ++scc)
{
trace << scc << ": " << scc_is_ba_type[scc] << " {";
for (auto s: si.states_of(scc))
trace << ' ' << s;
trace << " }\n";
}
#endif
unsigned nst = aut->num_states();
auto res = make_twa_graph(aut->get_dict());
res->copy_ap_of(aut);
res->prop_copy(aut, { true, false, false, true });
res->new_states(nst);
res->set_buchi();
res->set_init_state(aut->get_init_state_number());
trival deterministic = aut->prop_deterministic();
std::vector<unsigned> state_map(aut->num_states());
for (unsigned n = 0; n < scc_max; ++n)
{
auto states = si.states_of(n);
if (scc_is_ba_type[n])
{
// If the SCC is BA-type, we know exactly what state need to
// be marked as accepting.
for (auto s: states)
{
bool acc = ba_final_states[s];
for (auto& t: aut->out(s))
res->new_acc_edge(s, t.dst, t.cond, acc);
}
continue;
}
else
{
deterministic = false;
// The main copy is only accepting for inf_alone
// and for all Inf sets that have no matching Fin
// sets in this SCC.
acc_cond::mark_t sccsets = si.acc(n);
acc_cond::mark_t f = (sccsets << 1U) & inf_pairs;
acc_cond::mark_t i = sccsets & (inf_pairs | inf_alone);
i -= f;
for (auto s: states)
{
bool acc = aut->state_acc_sets(s) & i;
for (auto& t: aut->out(s))
res->new_acc_edge(s, t.dst, t.cond, acc);
}
auto rem = sccsets & ((inf_pairs >> 1U) | fin_alone);
assert(rem != 0U);
auto sets = rem.sets();
unsigned ss = states.size();
for (auto r: sets)
{
unsigned base = res->new_states(ss);
for (auto s: states)
state_map[s] = base++;
for (auto s: states)
{
auto ns = state_map[s];
acc_cond::mark_t acc = aut->state_acc_sets(s);
if (acc.has(r))
continue;
bool jacc = acc & inf_alone;
bool cacc = fin_alone.has(r) || acc.has(r + 1);
for (auto& t: aut->out(s))
{
if (si.scc_of(t.dst) != n)
continue;
auto nd = state_map[t.dst];
res->new_acc_edge(ns, nd, t.cond, cacc);
// We need only one non-deterministic jump per
// cycle. As an approximation, we only do
// them on back-links.
if (t.dst <= s)
res->new_acc_edge(s, nd, t.cond, jacc);
}
}
}
}
}
res->purge_dead_states();
res->prop_deterministic(deterministic);
return res;
}
static twa_graph_ptr
rabin_to_buchi_maybe(const const_twa_graph_ptr& aut)
{
if (!aut->prop_state_acc().is_true())
return nullptr;
auto code = aut->get_acceptance();
if (code.is_t())
return nullptr;
acc_cond::mark_t inf_pairs = 0U;
acc_cond::mark_t inf_alone = 0U;
acc_cond::mark_t fin_alone = 0U;
auto s = code.back().size;
// Rabin 1
if (code.back().op == acc_cond::acc_op::And && s == 4)
goto start_and;
// Co-Büchi
else if (code.back().op == acc_cond::acc_op::Fin && s == 1)
goto start_fin;
// Rabin >1
else if (code.back().op != acc_cond::acc_op::Or)
return nullptr;
while (s)
{
--s;
if (code[s].op == acc_cond::acc_op::And)
{
start_and:
auto o1 = code[--s].op;
auto m1 = code[--s].mark;
auto o2 = code[--s].op;
auto m2 = code[--s].mark;
// We expect
// Fin({n}) & Inf({n+1})
if (o1 != acc_cond::acc_op::Fin ||
o2 != acc_cond::acc_op::Inf ||
m1.count() != 1 ||
m2.count() != 1 ||
m2 != (m1 << 1U))
return nullptr;
inf_pairs |= m2;
}
else if (code[s].op == acc_cond::acc_op::Fin)
{
start_fin:
fin_alone |= code[--s].mark;
}
else if (code[s].op == acc_cond::acc_op::Inf)
{
auto m1 = code[--s].mark;
if (m1.count() != 1)
return nullptr;
inf_alone |= m1;
}
else
{
return nullptr;
}
}
trace << "inf_pairs: " << inf_pairs << '\n';
trace << "inf_alone: " << inf_alone << '\n';
trace << "fin_alone: " << fin_alone << '\n';
return ra_to_ba(aut, inf_pairs, inf_alone, fin_alone);
}
// If the DNF is
// Fin(1)&Inf(2)&Inf(4) | Fin(2)&Fin(3)&Inf(1) |
// Inf(1)&Inf(3) | Inf(1)&Inf(2) | Fin(4)
// this returns the following map:
// {1} => Inf(2)&Inf(4)
// {2,3} => Inf(1)
// {} => Inf(1)&Inf(3) | Inf(1)&Inf(2)
// {4} => t
static std::map<acc_cond::mark_t, acc_cond::acc_code>
split_dnf_acc_by_fin(const acc_cond::acc_code& acc)
{
std::map<acc_cond::mark_t, acc_cond::acc_code> res;
auto pos = &acc.back();
if (pos->op == acc_cond::acc_op::Or)
--pos;
auto start = &acc.front();
while (pos > start)
{
if (pos->op == acc_cond::acc_op::Fin)
{
// We have only a Fin term, without Inf. In this case
// only, the Fin() may encode a disjunction of sets.
for (auto s: pos[-1].mark.sets())
{
acc_cond::mark_t fin = 0U;
fin.set(s);
res[fin] = acc_cond::acc_code{};
}
pos -= pos->size + 1;
}
else
{
// We have a conjunction of Fin and Inf sets.
auto end = pos - pos->size - 1;
acc_cond::mark_t fin = 0U;
acc_cond::mark_t inf = 0U;
while (pos > end)
{
switch (pos->op)
{
case acc_cond::acc_op::And:
--pos;
break;
case acc_cond::acc_op::Fin:
fin |= pos[-1].mark;
assert(pos[-1].mark.count() == 1);
pos -= 2;
break;
case acc_cond::acc_op::Inf:
inf |= pos[-1].mark;
pos -= 2;
break;
case acc_cond::acc_op::FinNeg:
case acc_cond::acc_op::InfNeg:
case acc_cond::acc_op::Or:
SPOT_UNREACHABLE();
break;
}
}
assert(pos == end);
acc_cond::acc_word w[2];
w[0].mark = inf;
w[1].op = acc_cond::acc_op::Inf;
w[1].size = 1;
acc_cond::acc_code c;
c.insert(c.end(), w, w + 2);
auto p = res.emplace(fin, c);
if (!p.second)
p.first->second |= std::move(c);
}
}
return res;
}
static twa_graph_ptr
remove_fin_det_weak(const const_twa_graph_ptr& aut)
{
// Clone the original automaton.
auto res = make_twa_graph(aut,
{
true, // state based
true, // inherently weak
true, // determinisitic
true, // stutter inv.
});
res->purge_dead_states();
scc_info si(res);
// We will modify res in place, and the resulting
// automaton will only have one acceptance set.
acc_cond::mark_t all_acc = res->set_buchi();
res->prop_state_acc(true);
res->prop_deterministic(true);
unsigned sink = res->num_states();
for (unsigned src = 0; src < sink; ++src)
{
acc_cond::mark_t acc = 0U;
unsigned scc = si.scc_of(src);
if (si.is_accepting_scc(scc) && !si.is_trivial(scc))
acc = all_acc;
// Keep track of all conditions on edge leaving state
// SRC, so we can complete it.
bdd missingcond = bddtrue;
for (auto& t: res->out(src))
{
missingcond -= t.cond;
t.acc = acc;
}
// Complete the original automaton.
if (missingcond != bddfalse)
{
if (res->num_states() == sink)
{
res->new_state();
res->new_acc_edge(sink, sink, bddtrue);
}
res->new_edge(src, sink, missingcond);
}
}
//res->merge_edges();
return res;
}
}
twa_graph_ptr remove_fin(const const_twa_graph_ptr& aut)
{
if (!aut->acc().uses_fin_acceptance())
return std::const_pointer_cast<twa_graph>(aut);
// FIXME: we should check whether the automaton is weak.
if (aut->prop_inherently_weak().is_true() && is_deterministic(aut))
return remove_fin_det_weak(aut);
if (auto maybe = streett_to_generalized_buchi_maybe(aut))
return maybe;
if (auto maybe = rabin_to_buchi_maybe(aut))
return maybe;
std::vector<acc_cond::acc_code> code;
std::vector<acc_cond::mark_t> rem;
std::vector<acc_cond::mark_t> keep;
std::vector<acc_cond::mark_t> add;
bool has_true_term = false;
acc_cond::mark_t allinf = 0U;
acc_cond::mark_t allfin = 0U;
{
auto acccode = aut->get_acceptance();
if (!acccode.is_dnf())
acccode = acccode.to_dnf();
auto split = split_dnf_acc_by_fin(acccode);
auto sz = split.size();
assert(sz > 0);
rem.reserve(sz);
code.reserve(sz);
keep.reserve(sz);
add.reserve(sz);
for (auto p: split)
{
// The empty Fin should always come first
assert(p.first != 0U || rem.empty());
rem.push_back(p.first);
allfin |= p.first;
acc_cond::mark_t inf = 0U;
if (!p.second.empty())
{
auto pos = &p.second.back();
auto end = &p.second.front();
while (pos > end)
{
switch (pos->op)
{
case acc_cond::acc_op::And:
case acc_cond::acc_op::Or:
--pos;
break;
case acc_cond::acc_op::Inf:
inf |= pos[-1].mark;
pos -= 2;
break;
case acc_cond::acc_op::Fin:
case acc_cond::acc_op::FinNeg:
case acc_cond::acc_op::InfNeg:
SPOT_UNREACHABLE();
break;
}
}
}
if (inf == 0U)
{
has_true_term = true;
}
code.push_back(std::move(p.second));
keep.push_back(inf);
allinf |= inf;
add.push_back(0U);
}
}
assert(add.size() > 0);
acc_cond acc = aut->acc();
unsigned extra_sets = 0;
// Do we have common sets between the acceptance terms?
// If so, we need extra sets to distinguish the terms.
bool interference = false;
{
auto sz = keep.size();
acc_cond::mark_t sofar = 0U;
for (unsigned i = 0; i < sz; ++i)
{
auto k = keep[i];
if (k & sofar)
{
interference = true;
break;
}
sofar |= k;
}
if (interference)
{
trace << "We have interferences\n";
// We need extra set, but we will try
// to reuse the Fin number if they are
// not used as Inf as well.
std::vector<int> exs(acc.num_sets());
for (auto f: allfin.sets())
{
if (allinf.has(f)) // Already used as Inf
{
exs[f] = acc.add_set();
++extra_sets;
}
else
{
exs[f] = f;
}
}
for (unsigned i = 0; i < sz; ++i)
{
acc_cond::mark_t m = 0U;
for (auto f: rem[i].sets())
m.set(exs[f]);
trace << "rem[" << i << "] = " << rem[i]
<< " m = " << m << '\n';
add[i] = m;
code[i] &= acc.inf(m);
trace << "code[" << i << "] = " << code[i] << '\n';
}
}
else if (has_true_term)
{
trace << "We have a true term\n";
unsigned one = acc.add_sets(1);
extra_sets += 1;
acc_cond::mark_t m({one});
auto c = acc.inf(m);
for (unsigned i = 0; i < sz; ++i)
{
if (!code[i].is_t())
continue;
add[i] = m;
code[i] &= std::move(c);
c = acc.fin(0U); // Use false for the other terms.
trace << "code[" << i << "] = " << code[i] << '\n';
}
}
}
acc_cond::acc_code new_code = aut->acc().fin(0U);
for (auto c: code)
new_code |= std::move(c);
unsigned cs = code.size();
for (unsigned i = 0; i < cs; ++i)
trace << i << " Rem " << rem[i] << " Code " << code[i]
<< " Keep " << keep[i] << '\n';
unsigned nst = aut->num_states();
auto res = make_twa_graph(aut->get_dict());
res->copy_ap_of(aut);
res->prop_copy(aut, { true, false, false, true });
res->new_states(nst);
res->set_acceptance(aut->num_sets() + extra_sets, new_code);
res->set_init_state(aut->get_init_state_number());
bool sbacc = aut->prop_state_acc().is_true();
scc_info si(aut);
unsigned nscc = si.scc_count();
std::vector<unsigned> state_map(nst);
for (unsigned n = 0; n < nscc; ++n)
{
auto m = si.acc(n);
auto states = si.states_of(n);
trace << "SCC #" << n << " uses " << m << '\n';
// What to keep and add into the main copy
acc_cond::mark_t main_sets = 0U;
acc_cond::mark_t main_add = 0U;
bool intersects_fin = false;
for (unsigned i = 0; i < cs; ++i)
if (!(m & rem[i]))
{
main_sets |= keep[i];
main_add |= add[i];
}
else
{
intersects_fin = true;
}
trace << "main_sets " << main_sets << "\nmain_add " << main_add << '\n';
// Create the main copy
for (auto s: states)
for (auto& t: aut->out(s))
{
acc_cond::mark_t a = 0U;
if (sbacc || SPOT_LIKELY(si.scc_of(t.dst) == n))
a = (t.acc & main_sets) | main_add;
res->new_edge(s, t.dst, t.cond, a);
}
// We do not need any other copy if the SCC is non-accepting,
// of if it does not intersect any Fin.
if (!intersects_fin || si.is_rejecting_scc(n))
continue;
// Create clones
for (unsigned i = 0; i < cs; ++i)
if (m & rem[i])
{
auto r = rem[i];
trace << "rem[" << i << "] = " << r << " requires a copy\n";
unsigned base = res->new_states(states.size());
for (auto s: states)
state_map[s] = base++;
auto k = keep[i];
auto a = add[i];
for (auto s: states)
{
auto ns = state_map[s];
for (auto& t: aut->out(s))
{
if ((t.acc & r) || si.scc_of(t.dst) != n)
continue;
auto nd = state_map[t.dst];
res->new_edge(ns, nd, t.cond, (t.acc & k) | a);
// We need only one non-deterministic jump per
// cycle. As an approximation, we only do
// them on back-links.
if (t.dst <= s)
{
acc_cond::mark_t a = 0U;
if (sbacc)
a = (t.acc & main_sets) | main_add;
res->new_edge(s, nd, t.cond, a);
}
}
}
}
}
// If the input had no Inf, the output is a state-based automaton.
if (allinf == 0U)
res->prop_state_acc(true);
res->purge_dead_states();
trace << "before cleanup: " << res->get_acceptance() << '\n';
cleanup_acceptance_here(res);
trace << "after cleanup: " << res->get_acceptance() << '\n';
res->merge_edges();
return res;
}
}