spot/spot/twaalgos/alternation.cc
2025-10-15 16:32:03 +02:00

885 lines
28 KiB
C++

// -*- coding: utf-8 -*-
// Copyright (C) by the Spot authors, see the AUTHORS file for details.
//
// 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 "config.h"
#include <algorithm>
#include <sstream>
#include <spot/twaalgos/alternation.hh>
#include <spot/twaalgos/sccinfo.hh>
#include <spot/twaalgos/split.hh>
#include <spot/priv/robin_hood.hh>
#include <spot/misc/minato.hh>
#include <spot/misc/bddlt.hh>
namespace spot
{
outedge_combiner::outedge_combiner(const twa_graph_ptr& aut, unsigned sink)
: aut_(aut), vars_(bddtrue), acc_sink_(sink)
{
}
outedge_combiner::~outedge_combiner()
{
aut_->get_dict()->unregister_all_my_variables(this);
}
bdd outedge_combiner::operator()(unsigned st, const std::vector<unsigned>& dst_filter,
const std::vector<std::tuple<unsigned, bdd, unsigned>>& edge_filter,
bool remove_original_edges)
{
const auto& dict = aut_->get_dict();
bdd res = bddtrue;
for (unsigned d1: aut_->univ_dests(st))
{
bdd res2 = bddfalse;
for (auto& e: aut_->out(d1))
{
// handle edge filtering
if (!edge_filter.empty())
{
// Trying all univ dests for e, find if there was at least one
// compatible edge that was accepting in the original TFA
auto univ_dests = aut_->univ_dests(e.dst);
if (std::all_of(univ_dests.begin(), univ_dests.end(),
[&](unsigned dst) {
for (const auto& acc_e : edge_filter)
if(std::get<0>(acc_e) == e.src
&& std::get<2>(acc_e) == dst
&& bdd_implies(e.cond, std::get<1>(acc_e)))
return false; // false because we don't want to skip it
return true;
}))
continue;
}
else if (!dst_filter.empty()) // same for state-based acc
{
// if any edge destination is an accepting state in the SERE
// automaton, handle the edge, otherwise skip it
auto univ_dests = aut_->univ_dests(e.dst);
if (std::all_of(univ_dests.begin(), univ_dests.end(),
[&](unsigned dst)
{
return std::find(dst_filter.begin(), dst_filter.end(), dst)
== dst_filter.end();
}))
continue;
}
bdd out = bddtrue;
for (unsigned d: aut_->univ_dests(e.dst))
{
if (d == acc_sink_)
continue;
auto p = state_to_var.emplace(d, 0);
if (p.second)
{
int v = dict->register_anonymous_variables(1, this);
p.first->second = v;
var_to_state.emplace(v, d);
vars_ &= bdd_ithvar(v);
}
out &= bdd_ithvar(p.first->second);
}
res2 |= e.cond & out;
if (remove_original_edges)
e.cond = bddfalse;
}
res &= res2;
}
return res;
}
void outedge_combiner::new_dests(unsigned st, bdd out) const
{
minato_isop isop(out);
bdd cube;
std::vector<unsigned> univ_dest;
while ((cube = isop.next()) != bddfalse)
{
bdd cond = bdd_exist(cube, vars_);
bdd dest = bdd_existcomp(cube, vars_);
if (dest == bddtrue)
{
// if dest is bddtrue then the accepting sink is the only
// destination for this edge, in that case don't filter it out
assert(acc_sink_ != -1u);
aut_->new_edge(st, acc_sink_, cond);
continue;
}
do
{
assert(bdd_low(dest) == bddfalse);
auto it = var_to_state.find(bdd_var(dest));
assert(it != var_to_state.end());
univ_dest.push_back(it->second);
dest = bdd_high(dest);
}
while (dest != bddtrue);
std::sort(univ_dest.begin(), univ_dest.end());
aut_->new_univ_edge(st, univ_dest.begin(), univ_dest.end(), cond);
univ_dest.clear();
}
}
namespace
{
class alternation_remover final
{
protected:
const_twa_graph_ptr aut_;
scc_info si_;
enum scc_class : char { accept, reject_1, reject_more };
std::vector<scc_class> class_of_;
bool has_reject_more_ = false;
unsigned reject_1_count_ = 0;
std::set<unsigned> true_states_;
bool ensure_weak_scc(unsigned scc)
{
bool first = true;
bool reject_cycle = false;
acc_cond::mark_t m = {};
for (unsigned src: si_.states_of(scc))
for (auto& t: aut_->out(src))
for (unsigned d: aut_->univ_dests(t.dst))
if (si_.scc_of(d) == scc)
{
if (first)
{
first = false;
m = t.acc;
reject_cycle = !aut_->acc().accepting(m);
}
else if (m != t.acc)
{
throw std::runtime_error
("remove_alternation() only works with weak "
"alternating automata");
}
// In case of a universal edge we only
// need to check the first destination
// inside the SCC, because the other
// have the same t.acc.
break;
}
return reject_cycle;
}
void classify_each_scc()
{
auto& g = aut_->get_graph();
unsigned sc = si_.scc_count();
for (unsigned n = 0; n < sc; ++n)
{
if (si_.is_trivial(n))
continue;
if (si_.states_of(n).size() == 1)
{
if (si_.is_rejecting_scc(n))
{
class_of_[n] = scc_class::reject_1;
++reject_1_count_;
}
else
{
// For size one, scc_info should always be able to
// decide rejecting/accepting.
assert(si_.is_accepting_scc(n));
// Catch unsupported types of automata
bool rejecting = ensure_weak_scc(n);
assert(!rejecting);
(void) rejecting;
// Detect if it is a "true state"
unsigned s = si_.states_of(n).front();
auto& ss = g.state_storage(s);
if (ss.succ == ss.succ_tail)
{
auto& es = g.edge_storage(ss.succ);
if (es.cond == bddtrue && !aut_->is_univ_dest(es.dst))
true_states_.emplace(s);
}
}
}
else if (ensure_weak_scc(n))
{
class_of_[n] = reject_more;
has_reject_more_ = true;
}
}
}
std::vector<int> state_to_var_;
std::map<int, unsigned> var_to_state_;
std::vector<int> scc_to_var_;
std::map<int, acc_cond::mark_t> var_to_mark_;
std::vector<unsigned> mark_to_state_;
bdd all_vars_;
bdd all_marks_;
bdd all_states_;
void allocate_state_vars()
{
auto d = aut_->get_dict();
// We need one BDD variable per possible output state. If
// that state is in a reject_more SCC we actually use two
// variables for the breakpoint.
unsigned ns = aut_->num_states();
state_to_var_.reserve(ns);
bdd all_states = bddtrue;
for (unsigned s = 0; s < ns; ++s)
{
if (!si_.reachable_state(s))
{
state_to_var_.push_back(0);
continue;
}
scc_class c = class_of_[si_.scc_of(s)];
bool r = c == scc_class::reject_more;
int v = d->register_anonymous_variables(1 + r, this);
state_to_var_.push_back(v);
var_to_state_[v] = s;
all_states &= bdd_ithvar(v);
if (r)
{
var_to_state_[v + 1] = ~s;
all_states &= bdd_ithvar(v + 1);
}
}
// We also use one BDD variable per reject_1 SCC. Each of
// these variables will represent a bit in mark_t. We reserve
// the first bit for the break_point construction if we have
// some reject_more SCC.
unsigned nc = si_.scc_count();
scc_to_var_.reserve(nc);
unsigned mark_pos = has_reject_more_;
mark_to_state_.resize(mark_pos);
bdd all_marks = bddtrue;
for (unsigned s = 0; s < nc; ++s)
{
scc_class c = class_of_[s];
if (c == scc_class::reject_1)
{
int v = d->register_anonymous_variables(1, this);
scc_to_var_.emplace_back(v);
mark_to_state_.push_back(si_.one_state_of(s));
var_to_mark_.emplace(v, acc_cond::mark_t({mark_pos++}));
bdd bv = bdd_ithvar(v);
all_marks &= bv;
}
else
{
scc_to_var_.emplace_back(0);
}
}
all_marks_ = all_marks;
all_states_ = all_states;
all_vars_ = all_states & all_marks;
}
std::map<unsigned, bdd> state_as_bdd_cache_;
bdd state_as_bdd(unsigned s)
{
auto p = state_as_bdd_cache_.insert({s, bddfalse});
if (!p.second)
return p.first->second;
bool marked = (int)s < 0;
if (marked)
s = ~s;
unsigned scc_s = si_.scc_of(s);
bdd res = bddfalse;
for (auto& e: aut_->out(s))
{
bdd dest = bddtrue;
for (unsigned d: aut_->univ_dests(e.dst))
{
unsigned scc_d = si_.scc_of(d);
scc_class c = class_of_[scc_d];
bool mark =
marked && (scc_s == scc_d) && (c == scc_class::reject_more);
dest &= bdd_ithvar(state_to_var_[d] + mark);
if (c == scc_class::reject_1 && scc_s == scc_d)
dest &= bdd_ithvar(scc_to_var_[scc_d]);
}
res |= e.cond & dest;
}
p.first->second = res;
return res;
}
acc_cond::mark_t bdd_to_state(bdd b, std::vector<unsigned>& s)
{
acc_cond::mark_t m = {};
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
{
auto it2 = var_to_mark_.find(v);
assert(it2 != var_to_mark_.end());
m |= it2->second;
}
b = bdd_high(b);
}
return m;
}
void simplify_state_set(std::vector<unsigned>& ss)
{
auto to_remove = true_states_;
for (unsigned i: ss)
if ((int)i < 0)
to_remove.emplace(~i);
auto i =
std::remove_if(ss.begin(), ss.end(),
[&] (unsigned s) {
return to_remove.find(s) != to_remove.end();
});
ss.erase(i, ss.end());
std::sort(ss.begin(), ss.end());
}
bool has_mark(const std::vector<unsigned>& ss)
{
for (unsigned i: ss)
if ((int)i < 0)
return true;
return false;
}
void set_mark(std::vector<unsigned>& ss)
{
for (unsigned& s: ss)
if (class_of_[si_.scc_of(s)] == scc_class::reject_more)
s = ~s;
}
public:
alternation_remover(const const_twa_graph_ptr& aut)
: aut_(aut), si_(aut, scc_info_options::TRACK_STATES),
class_of_(si_.scc_count(), scc_class::accept)
{
}
~alternation_remover()
{
aut_->get_dict()->unregister_all_my_variables(this);
}
twa_graph_ptr run(bool named_states, const output_aborter* aborter,
bool raise_if_too_many_sets)
{
// First, we classify each SCC into three possible classes:
//
// 1) trivial or accepting
// 2) rejecting of size 1
// 3) rejecting of size >1
classify_each_scc();
if (!raise_if_too_many_sets &&
(has_reject_more_ + reject_1_count_) > SPOT_MAX_ACCSETS)
return nullptr;
// Rejecting SCCs of size 1 can be handled using generalized
// Büchi acceptance, using one set per SCC, as in Gastin &
// Oddoux CAV'01. See also Boker & et al. ICALP'10. Larger
// rejecting SCCs require a more expensive procedure known as
// the break point construction. See Miyano & Hayashi (TCS
// 1984). We are currently combining the two constructions.
auto res = make_twa_graph(aut_->get_dict());
res->copy_ap_of(aut_);
// We preserve deterministic-like properties, and
// stutter-invariance.
res->prop_copy(aut_, {false, false, false, true, true, true});
// This will raise an exception if we request too many sets.
res->set_generalized_buchi(has_reject_more_ + reject_1_count_);
// Before we start, let's decide how we will iterate on the
// BDD that we use to encode the transition function. We have
// two way of doing so: iterating over 2^AP, or precomputing a
// set of "separated labels" that cover all labels. The
// latter is a good idea if that set is much smaller than
// 2^AP, but we cannot always know that before hand.
std::vector<bdd> separated_labels;
unsigned n_ap = aut_->ap().size();
// If |AP| is small, don't bother with the computation of
// separated labels.
bool will_use_labels = n_ap > 5;
if (will_use_labels)
{
edge_separator es;
// Gather all labels, but stop if we see too many.
// The threshold below is arbitrary.
will_use_labels = es.add_to_basis(aut_, 256 * n_ap);
if (will_use_labels)
separated_labels = es.basis();
}
// We for easier computation of outgoing sets, we will
// represent states using BDD variables.
allocate_state_vars();
// Conversion between state-sets and states.
typedef std::vector<unsigned> state_set;
std::vector<state_set> s_to_ss;
std::map<state_set, unsigned> ss_to_s;
std::stack<unsigned> todo;
std::vector<std::string>* state_name = nullptr;
if (named_states)
{
state_name = new std::vector<std::string>();
res->set_named_prop("state-names", state_name);
}
auto new_state = [&](state_set& ss, bool& need_mark)
{
simplify_state_set(ss);
if (has_reject_more_)
{
need_mark = has_mark(ss);
if (!need_mark)
set_mark(ss);
}
auto p = ss_to_s.emplace(ss, 0);
if (!p.second)
return p.first->second;
unsigned s = res->new_state();
assert(s == s_to_ss.size());
p.first->second = s;
s_to_ss.emplace_back(ss);
todo.emplace(s);
if (named_states)
{
std::ostringstream os;
bool notfirst = false;
for (unsigned s: ss)
{
if (notfirst)
os << ',';
else
notfirst = true;
if ((int)s < 0)
{
os << '~';
s = ~s;
}
os << s;
}
if (!notfirst)
os << "{}";
state_name->emplace_back(os.str());
}
return s;
};
const auto& i = aut_->univ_dests(aut_->get_init_state_number());
state_set is(i.begin(), i.end());
bool has_mark = false;
res->set_init_state(new_state(is, has_mark));
acc_cond::mark_t all_marks = res->acc().all_sets();
// We use a cache to avoid the costly loop around
// separated_labels.
//
// Cache entries have the form (bdd, [begin, end]) where bdd
// what should be split, and begin/end denotes a range of
// existing transition numbers that cover the split.
//
// std::pair causes some noexcept warnings when used in
// robin_hood::unordered_map with GCC 9.4. Use robin_hood::pair
// instead.
typedef robin_hood::pair<unsigned, unsigned> cached_t;
robin_hood::unordered_map<bdd, cached_t, bdd_hash> split_cond;
state_set v;
while (!todo.empty())
{
if (aborter && aborter->too_large(res))
return nullptr;
unsigned s = todo.top();
todo.pop();
bdd bs = bddtrue;
for (unsigned se: s_to_ss[s])
bs &= state_as_bdd(se);
bdd ap = bdd_exist(bdd_support(bs), all_vars_);
bdd all_letters = bdd_exist(bs, all_vars_);
// Given a label, and BDD expression representing
// the combination of destinations, create the edges.
auto create_edges = [&](bdd label, bdd dest_formula)
{
minato_isop isop(dest_formula);
bdd dest;
while ((dest = isop.next()) != bddfalse)
{
v.clear();
acc_cond::mark_t m = bdd_to_state(dest, v);
// if there is no promise "f" between a state
// that does not have f, and a state that have
// "f", we can add one. Doing so will help later
// simplifications performed by postprocessor. An
// example where this is needed is the VWAA
// generated by ltl[23]ba for GFa. Without the
// next loop, the final TGBA has 2 states instead
// of 1.
for (unsigned m1: (all_marks - m).sets())
{
if (has_reject_more_ && m1 == 0)
continue;
auto& sv = s_to_ss[s];
unsigned ms = mark_to_state_[m1];
if (std::find(v.begin(), v.end(), ms) != v.end())
{
unsigned ms = mark_to_state_[m1];
if (std::find(sv.begin(), sv.end(), ms) == sv.end())
m.set(m1);
}
}
unsigned d = new_state(v, has_mark);
if (has_mark)
m.set(0);
res->new_edge(s, d, label, all_marks - m);
}
};
if (!will_use_labels)
{
// Loop over all possible valuations of atomic properties.
for (bdd oneletter: minterms_of(all_letters, ap))
create_edges(oneletter, bdd_restrict(bs, oneletter));
}
else
{
auto& [begin, end] = split_cond[all_letters];
if (begin == end)
{
begin = res->num_edges() + 1;
for (bdd label: separated_labels)
create_edges(label, bdd_relprod(label, bs,
res->ap_vars()));
end = res->num_edges() + 1;
}
else
{
// We have already split all_letters once, so we
// can simply reuse the set of labels we used
// then, avoiding the iteration on
// separated_labels.
auto& g = res->get_graph();
bdd last = bddfalse;
for (unsigned i = begin; i < end; ++i)
{
bdd label = g.edge_storage(i).cond;
if (label == last)
continue;
last = label;
create_edges(label, bdd_relprod(label, bs,
res->ap_vars()));
}
}
}
}
res->merge_edges();
return res;
}
};
}
twa_graph_ptr remove_alternation(const const_twa_graph_ptr& aut,
bool named_states,
const output_aborter* aborter,
bool raise_if_too_many_sets)
{
if (aut->is_existential())
// Nothing to do, why was this function called at all?
return std::const_pointer_cast<twa_graph>(aut);
alternation_remover ar(aut);
return ar.run(named_states, aborter, raise_if_too_many_sets);
}
// On-the-fly alternating Büchi automaton to nondeterministic Büchi automaton
// using the breakpoint construction.
univ_remover_state::univ_remover_state(const std::set<unsigned>& states)
: is_reset_(false)
{
is_reset_ = std::all_of(states.begin(), states.end(),
[] (unsigned s) { return int(s) < 0; });
// When all states are marked (i.e. Q0 is empty), the state is in reset
// mode, meaning that it is an accepting state.
// The states can immediately be unmarked, since the acceptance mark is
// held by the incoming transition.
if (is_reset_)
for (unsigned s : states)
states_.insert(~s);
else
states_ = states;
}
int univ_remover_state::compare(const state* other) const
{
const auto o = down_cast<const univ_remover_state*>(other);
assert(o);
if (states_ < o->states())
return -1;
if (states_ > o->states())
return 1;
return 0;
}
size_t univ_remover_state::hash() const
{
size_t hash = 0;
for (unsigned s : states_)
hash ^= wang32_hash(s);
return hash;
}
state* univ_remover_state::clone() const
{
return new univ_remover_state(*this);
}
const std::set<unsigned>& univ_remover_state::states() const
{
return states_;
}
bool univ_remover_state::is_reset() const
{
return is_reset_;
}
class univ_remover_succ_iterator : public twa_succ_iterator
{
private:
bdd transitions_;
bdd all_states_;
bdd ap_;
bdd all_letters_;
bdd dest_;
bdd cond_;
minato_isop isop_;
const std::map<int, unsigned>& var_to_state_;
univ_remover_state* dst_;
public:
univ_remover_succ_iterator(const_twa_graph_ptr aut,
const univ_remover_state* state,
const std::vector<int>& state_to_var,
const std::map<int, unsigned>& var_to_state,
bdd all_states)
: transitions_(bddtrue), all_states_(all_states), dest_(bddfalse),
cond_(bddfalse), isop_(bddfalse), var_to_state_(var_to_state)
{
// Build the bdd transitions_, from which we extract the successors.
for (unsigned s : state->states())
{
bdd state_bdd = bddfalse;
bool marked = (int)s < 0;
if (marked)
s = ~s;
for (const auto& e : aut->out(s))
{
bdd univ_bdd = bddtrue;
for (const auto& d : aut->univ_dests(e.dst))
univ_bdd &= bdd_ithvar(state_to_var[d] + (marked || e.acc));
state_bdd |= e.cond & univ_bdd;
}
transitions_ &= state_bdd;
}
ap_ = bdd_exist(bdd_support(transitions_), all_states_);
all_letters_ = bdd_exist(transitions_, all_states_);
}
std::set<unsigned> bdd_to_state(bdd b) const
{
std::set<unsigned> state;
while (b != bddtrue)
{
assert(bdd_low(b) == bddfalse);
int v = bdd_var(b);
b = bdd_high(b);
auto it = var_to_state_.find(v);
assert(it != var_to_state_.end());
state.insert(it->second);
}
return state;
}
void one_transition()
{
dest_ = isop_.next();
if (dest_ != bddfalse || all_letters_ != bddfalse)
{
// If it was the last transition, try the next letter.
if (dest_ == bddfalse)
{
bdd oneletter = bdd_satoneset(all_letters_, ap_, bddfalse);
cond_ = oneletter;
all_letters_ -= oneletter;
// Get a sum of possible transitions matching this letter.
isop_ = minato_isop(bdd_restrict(transitions_, oneletter));
dest_ = isop_.next();
}
std::set<unsigned> dest = bdd_to_state(dest_);
dst_ = new univ_remover_state(dest);
}
}
virtual bool first() override
{
one_transition();
return dest_ != bddfalse;
}
virtual bool next() override
{
one_transition();
return dest_ != bddfalse;
}
virtual bool done() const override
{
return dest_ == bddfalse && all_letters_ == bddfalse;
}
virtual const state* dst() const override
{
return dst_;
}
virtual bdd cond() const override
{
return cond_;
}
virtual acc_cond::mark_t acc() const override
{
assert(dst_);
return dst_->is_reset() ?
acc_cond::mark_t({0}) :
acc_cond::mark_t({});
}
};
twa_univ_remover::twa_univ_remover(const const_twa_graph_ptr& aut)
: twa(aut->get_dict()), aut_(aut)
{
assert(aut->num_sets() == 1);
allocate_state_vars();
}
void twa_univ_remover::allocate_state_vars()
{
auto d = aut_->get_dict();
unsigned ns = aut_->num_states();
state_to_var_.reserve(ns);
all_states_ = bddtrue;
bdd all_vars = bddtrue;
for (unsigned s = 0; s < ns; ++s)
{
int v = d->register_anonymous_variables(2, this);
// v and v + 1 respectively correspond to state s and ~s, i.e. s \in Q0
// or s \in Q1 using the original paper's notation.
all_states_ &= bdd_ithvar(v) & bdd_ithvar(v + 1);
state_to_var_.push_back(v);
var_to_state_[v] = s;
var_to_state_[v + 1] = ~s;
}
}
const state* twa_univ_remover::get_init_state() const
{
std::set<unsigned> state;
for (unsigned i : aut_->univ_dests(aut_->get_init_state_number()))
state.insert(i);
return new univ_remover_state(state);
}
twa_succ_iterator* twa_univ_remover::succ_iter(const state* s) const
{
auto as = down_cast<const univ_remover_state*>(s);
assert(as);
return new univ_remover_succ_iterator(aut_, as, state_to_var_,
var_to_state_, all_states_);
}
std::string twa_univ_remover::format_state(const state* s) const
{
auto as = down_cast<const univ_remover_state*>(s);
std::ostringstream fmt;
bool first = true;
for (unsigned s : as->states())
{
if (!first)
fmt << ',';
else
first = false;
if ((int) s < 0)
fmt << '~' << ~s;
else
fmt << s;
}
return fmt.str();
}
twa_univ_remover_ptr remove_univ_otf(const const_twa_graph_ptr& aut)
{
assert(aut->acc().is_buchi());
auto res = std::make_shared<twa_univ_remover>(aut);
res->copy_ap_of(aut);
res->copy_acceptance_of(aut);
return res;
}
}