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spot/spot/tl/derive.cc

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// -*- coding: utf-8 -*-
// Copyright (C) 2021 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 "config.h"
#include <spot/priv/robin_hood.hh>
#include <spot/tl/derive.hh>
#include <spot/twa/bdddict.hh>
#include <spot/twa/formula2bdd.hh>
#include <spot/twaalgos/remprop.hh>
namespace spot
{
namespace
{
static std::vector<std::string>
formula_aps(formula f)
{
auto res = std::unordered_set<std::string>();
f.traverse([&res](formula f)
{
if (f.is(op::ap))
{
res.insert(f.ap_name());
return true;
}
return false;
});
return std::vector(res.begin(), res.end());
}
}
formula
rewrite_and_nlm(formula f)
{
unsigned s = f.size();
std::vector<formula> final;
std::vector<formula> non_final;
for (auto g: f)
if (g.accepts_eword())
final.emplace_back(g);
else
non_final.emplace_back(g);
if (non_final.empty())
// (a* & b*);c = (a*|b*);c
return formula::OrRat(std::move(final));
if (!final.empty())
{
// let F_i be final formulae
// N_i be non final formula
// (F_1 & ... & F_n & N_1 & ... & N_m)
// = (F_1 | ... | F_n);[*] && (N_1 & ... & N_m)
// | (F_1 | ... | F_n) && (N_1 & ... & N_m);[*]
formula f = formula::OrRat(std::move(final));
formula n = formula::AndNLM(std::move(non_final));
formula t = formula::one_star();
formula ft = formula::Concat({f, t});
formula nt = formula::Concat({n, t});
formula ftn = formula::AndRat({ft, n});
formula fnt = formula::AndRat({f, nt});
return formula::OrRat({ftn, fnt});
}
// No final formula.
// Translate N_1 & N_2 & ... & N_n into
// N_1 && (N_2;[*]) && ... && (N_n;[*])
// | (N_1;[*]) && N_2 && ... && (N_n;[*])
// | (N_1;[*]) && (N_2;[*]) && ... && N_n
formula star = formula::one_star();
std::vector<formula> disj;
for (unsigned n = 0; n < s; ++n)
{
std::vector<formula> conj;
for (unsigned m = 0; m < s; ++m)
{
formula g = f[m];
if (n != m)
g = formula::Concat({g, star});
conj.emplace_back(g);
}
disj.emplace_back(formula::AndRat(std::move(conj)));
}
return formula::OrRat(std::move(disj));
}
twa_graph_ptr
derive_finite_automaton(formula f, bool deterministic)
{
auto bdd_dict = make_bdd_dict();
auto aut = make_twa_graph(bdd_dict);
aut->prop_state_acc(true);
const auto acc_mark = aut->set_buchi();
auto formula2state = robin_hood::unordered_map<formula, unsigned>();
unsigned init_state = aut->new_state();
aut->set_init_state(init_state);
formula2state.insert({ f, init_state });
auto f_aps = formula_aps(f);
for (auto& ap : f_aps)
aut->register_ap(ap);
bdd all_aps = aut->ap_vars();
auto todo = std::vector<std::pair<formula, unsigned>>();
todo.push_back({f, init_state});
auto state_names = new std::vector<std::string>();
std::ostringstream ss;
ss << f;
state_names->push_back(ss.str());
auto find_dst = [&](formula derivative) -> unsigned
{
unsigned dst;
auto it = formula2state.find(derivative);
if (it != formula2state.end())
{
dst = it->second;
}
else
{
dst = aut->new_state();
todo.push_back({derivative, dst});
formula2state.insert({derivative, dst});
std::ostringstream ss;
ss << derivative;
state_names->push_back(ss.str());
}
return dst;
};
while (!todo.empty())
{
auto [curr_f, curr_state] = todo[todo.size() - 1];
todo.pop_back();
auto curr_acc_mark = curr_f.accepts_eword()
? acc_mark
: acc_cond::mark_t();
for (const bdd one : minterms_of(bddtrue, all_aps))
{
formula derivative =
partial_derivation(curr_f, one, bdd_dict, aut.get());
// no transition possible from this letter
if (derivative.is(op::ff))
continue;
// either the formula isn't an OrRat, or if it is we consider it as
// as a whole to get a deterministic automaton
if (deterministic || !derivative.is(op::OrRat))
{
auto dst = find_dst(derivative);
aut->new_edge(curr_state, dst, one, curr_acc_mark);
continue;
}
// formula is an OrRat and we want a non deterministic automaton,
// so consider each child as a destination
for (const auto& subformula : derivative)
{
auto dst = find_dst(subformula);
aut->new_edge(curr_state, dst, one, curr_acc_mark);
}
}
// if state has no transitions and should be accepting, create
// artificial transition
if (aut->get_graph().state_storage(curr_state).succ == 0
&& curr_f.accepts_eword())
aut->new_edge(curr_state, curr_state, bddfalse, acc_mark);
}
aut->set_named_prop("state-names", state_names);
aut->merge_edges();
return aut;
}
twa_graph_ptr
derive_automaton(formula f, bool deterministic)
{
auto finite = derive_finite_automaton(f, deterministic);
return from_finite(finite);
}
formula
partial_derivation(formula f, const bdd var, const bdd_dict_ptr& d,
void* owner)
{
if (f.is_boolean())
{
auto f_bdd = formula_to_bdd(f, d, owner);
if (bdd_implies(var, f_bdd))
return formula::eword();
return formula::ff();
}
switch (f.kind())
{
// handled by is_boolean above
case op::ff:
case op::tt:
case op::ap:
SPOT_UNREACHABLE();
case op::eword:
return formula::ff();
// d(E.F) = { d(E).F } U { c(E).d(F) }
case op::Concat:
{
formula E = f[0];
formula F = f.all_but(0);
auto res =
formula::Concat({ partial_derivation(E, var, d, owner), F });
if (E.accepts_eword())
res = formula::OrRat(
{ res, partial_derivation(F, var, d, owner) });
return res;
}
// d(E*) = d(E).E*
// d(E[*i..j]) = d(E).E[*(i-1)..(j-1)]
case op::Star:
{
auto min = f.min() == 0 ? 0 : (f.min() - 1);
auto max = f.max() == formula::unbounded()
? formula::unbounded()
: (f.max() - 1);
formula d_E = partial_derivation(f[0], var, d, owner);
return formula::Concat({ d_E, formula::Star(f[0], min, max) });
}
// d(E[:*i..j]) = E:E[:*(i-1)..(j-1)] + (eword if i == 0 or c(d(E)))
case op::FStar:
{
formula E = f[0];
if (f.min() == 0 && f.max() == 0)
return formula::tt();
auto d_E = partial_derivation(E, var, d, owner);
auto min = f.min() == 0 ? 0 : (f.min() - 1);
auto max = f.max() == formula::unbounded()
? formula::unbounded()
: (f.max() - 1);
auto results = std::vector<formula>();
auto E_i_j_minus = formula::FStar(E, min, max);
results.push_back(formula::Fusion({ d_E, E_i_j_minus }));
if (d_E.accepts_eword())
results.push_back(d_E);
if (f.min() == 0)
results.push_back(formula::eword());
return formula::OrRat(std::move(results));
}
// d(E && F) = d(E) && d(F)
// d(E + F) = {d(E)} U {d(F)}
case op::AndRat:
case op::OrRat:
{
std::vector<formula> subderivations;
for (auto subformula : f)
{
auto subderivation =
partial_derivation(subformula, var, d, owner);
subderivations.push_back(subderivation);
}
return formula::multop(f.kind(), std::move(subderivations));
}
// d(E:F) = {d(E):F} U {c(d(E)).d(F)}
case op::Fusion:
{
formula E = f[0];
formula F = f.all_but(0);
auto d_E = partial_derivation(E, var, d, owner);
auto res = formula::Fusion({ d_E, F });
if (d_E.accepts_eword())
res =
formula::OrRat({ res, partial_derivation(F, var, d, owner) });
return res;
}
case op::first_match:
{
formula E = f[0];
auto d_E = partial_derivation(E, var, d, owner);
// if d_E.accepts_eword(), first_match(d_E) will return eword
return formula::first_match(d_E);
}
default:
std::cerr << "unimplemented kind "
<< static_cast<int>(f.kind())
<< std::endl;
SPOT_UNIMPLEMENTED();
}
return formula::ff();
}
}
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