remfin: deal with almost-Rabin automata
I.e., automata that could be Rabin if we add some empty Fin(x) or full Inf(y) sets. This way it does not matter when remove_fin() is called after cleanup_acceptance(). * src/twaalgos/remfin.cc: Implement that. * src/tests/remfin.test: More tests.
This commit is contained in:
Alexandre Duret-Lutz
parent
ef1bbfc659
commit
5f0b6dc36c
2 changed files with 376 additions and 37 deletions
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@ -51,7 +51,8 @@ namespace spot
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is_scc_ba_type(const const_twa_graph_ptr& aut,
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const std::vector<unsigned>& states,
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std::vector<bool>& final,
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acc_cond::mark_t inf,
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acc_cond::mark_t inf_pairs,
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acc_cond::mark_t inf_alone,
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acc_cond::mark_t sets)
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{
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// Consider the SCC as one large cycle and check its
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@ -61,8 +62,8 @@ namespace spot
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// Let f=[F₁,F₂,...] and i=[I₁,I₂,...] be bitvectors where bit
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// Fᵢ (resp. Iᵢ) indicates that Fᵢ (resp. Iᵢ) has been visited
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// in the SCC.
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acc_cond::mark_t f = (sets << 1) & inf;
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acc_cond::mark_t i = sets & inf;
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acc_cond::mark_t f = (sets << 1) & inf_pairs;
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acc_cond::mark_t i = sets & inf_pairs;
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// If we have i&!f = [0,0,...] that means that the cycle formed
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// by the entire SCC is not accepting. However that does not
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// necessarily imply that all cycles in the SCC are also
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@ -70,6 +71,7 @@ namespace spot
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// accepting, but which becomes non-accepting when extended with
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// more states.
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i -= f;
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i |= (inf_alone & sets);
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if (!i)
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{
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// Check whether the SCC is accepting. We do that by simply
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@ -85,9 +87,9 @@ namespace spot
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// procedure, because empty() will call to_tgba() wich will
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// call remove_fin()...
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sccaut->prop_state_based_acc(false);
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// If SCCAUT is empty, the SCC is DBA realizable (and none
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// If SCCAUT is empty, the SCC is BA-type (and none
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// of its states are final). If SCCAUT is nonempty, the SCC
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// is not DBA realizable.
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// is not BA type.
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return sccaut->is_empty();
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}
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// The bits remaining sets in i corresponds to I₁s that have
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@ -120,7 +122,7 @@ namespace spot
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if (si.is_rejecting_scc(scc)) // this includes trivial SCCs
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continue;
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if (!is_scc_ba_type(aut, si.states_of(scc),
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final, inf, si.acc(scc)))
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final, inf_pairs, 0U, si.acc(scc)))
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return false;
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}
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}
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@ -145,13 +147,14 @@ namespace spot
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// Büchi-typeness of the SCC, but the resulting automaton should
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// be correct nonetheless.
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static twa_graph_ptr
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ra_to_ba(const const_twa_graph_ptr& aut)
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ra_to_ba(const const_twa_graph_ptr& aut,
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acc_cond::mark_t inf_pairs,
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acc_cond::mark_t inf_alone,
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acc_cond::mark_t fin_alone)
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{
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assert(aut->has_state_based_acc());
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assert(aut->acc().is_rabin() > 0);
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scc_info si(aut);
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// For state-based Rabin automata, we check each SCC for
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// BA-typeness. If an SCC is BA-type, its final states are stored
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// in BA_FINAL_STATES.
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@ -159,11 +162,13 @@ namespace spot
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bool ba_type = false;
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std::vector<bool> ba_final_states;
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#ifdef DEBUG
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acc_cond::mark_t fin;
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acc_cond::mark_t inf;
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std::tie(inf, fin) = aut->get_acceptance().used_inf_fin_sets();
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assert((fin << 1) == inf);
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assert(inf == (inf_pairs | inf_alone));
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assert(fin == ((inf_pairs >> 1) | fin_alone));
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#endif
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ba_final_states.resize(aut->num_states(), false);
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ba_type = true; // until proven otherwise
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unsigned scc_max = si.scc_count();
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@ -174,14 +179,36 @@ namespace spot
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scc_is_ba_type[scc] = true;
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continue;
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}
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bool scc_ba_type =
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is_scc_ba_type(aut, si.states_of(scc),
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ba_final_states, inf, si.acc(scc));
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bool scc_ba_type = false;
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auto sets = si.acc(scc);
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// If there is one fin_alone that is not in the SCC,
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// any cycle in the SCC is accepting. Mark all states
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// as final.
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if ((sets & fin_alone) != fin_alone)
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{
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for (auto s: si.states_of(scc))
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ba_final_states[s] = true;
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scc_ba_type = true;
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}
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// Conversely, if all fin_alone appear in the SCC, then it
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// cannot be accepting.
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else if (sets & fin_alone)
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{
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scc_ba_type = false;
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}
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// In the generale case (no fin_alone involved), we need
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// a dedicated check.
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else
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{
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scc_ba_type = is_scc_ba_type(aut, si.states_of(scc),
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ba_final_states,
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inf_pairs, inf_alone, si.acc(scc));
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}
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ba_type &= scc_ba_type;
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scc_is_ba_type[scc] = scc_ba_type;
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}
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#if TRACE
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#ifdef TRACE
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trace << "SCC DBA-realizibility\n";
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for (unsigned scc = 0; scc < scc_max; ++scc)
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{
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@ -197,8 +224,9 @@ namespace spot
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res->copy_ap_of(aut);
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res->prop_copy(aut, { true, false, false, true });
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res->new_states(nst);
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auto final_acc = res->set_buchi();
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res->set_buchi();
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res->set_init_state(aut->get_init_state_number());
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bool deterministic = aut->is_deterministic();
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std::vector<unsigned> state_map(aut->num_states());
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for (unsigned n = 0; n < scc_max; ++n)
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@ -211,25 +239,32 @@ namespace spot
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// be marked as accepting.
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for (auto s: states)
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{
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acc_cond::mark_t acc = 0U;
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if (ba_final_states[s])
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acc = final_acc;
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bool acc = ba_final_states[s];
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for (auto& t: aut->out(s))
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res->new_edge(s, t.dst, t.cond, acc);
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res->new_acc_edge(s, t.dst, t.cond, acc);
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}
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continue;
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}
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else
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{
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// The main copy is unaccepting
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for (auto s: states)
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for (auto& t: aut->out(s))
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res->new_edge(s, t.dst, t.cond);
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deterministic = false;
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auto rem = si.acc(n) & fin;
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if (!rem)
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// No Fin sets used in this SCC.
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continue;
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// The main copy is only accepting for inf_alone
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// and for all Inf sets that have no matching Fin
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// sets in this SCC.
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acc_cond::mark_t sccsets = si.acc(n);
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acc_cond::mark_t f = (sccsets << 1) & inf_pairs;
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acc_cond::mark_t i = sccsets & (inf_pairs | inf_alone);
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i -= f;
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for (auto s: states)
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{
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bool acc = aut->state_acc_sets(s) & i;
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for (auto& t: aut->out(s))
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res->new_acc_edge(s, t.dst, t.cond, acc);
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}
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auto rem = sccsets & ((inf_pairs >> 1) | fin_alone);
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assert(rem != 0U);
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auto sets = rem.sets();
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unsigned ss = states.size();
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@ -245,26 +280,102 @@ namespace spot
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acc_cond::mark_t acc = aut->state_acc_sets(s);
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if (acc.has(r))
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continue;
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bool jacc = acc & inf_alone;
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bool cacc = fin_alone.has(r) || acc.has(r + 1);
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for (auto& t: aut->out(s))
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{
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if (si.scc_of(t.dst) != n)
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continue;
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auto nd = state_map[t.dst];
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res->new_acc_edge(ns, nd, t.cond, t.acc.has(r + 1));
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res->new_acc_edge(ns, nd, t.cond, cacc);
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// We need only one non-deterministic jump per
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// cycle. As an approximation, we only do
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// them on back-links.
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if (t.dst <= s)
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res->new_edge(s, nd, t.cond);
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res->new_acc_edge(s, nd, t.cond, jacc);
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}
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}
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}
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}
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}
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res->purge_dead_states();
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res->prop_deterministic(deterministic);
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return res;
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}
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static twa_graph_ptr
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rabin_to_buchi_maybe(const const_twa_graph_ptr& aut)
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{
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if (!aut->has_state_based_acc())
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return nullptr;
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auto code = aut->get_acceptance();
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if (code.is_true())
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return nullptr;
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acc_cond::mark_t inf_pairs = 0U;
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acc_cond::mark_t inf_alone = 0U;
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acc_cond::mark_t fin_alone = 0U;
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auto s = code.back().size;
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// Rabin 1
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if (code.back().op == acc_cond::acc_op::And && s == 4)
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goto start_and;
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// Co-Büchi
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else if (code.back().op == acc_cond::acc_op::Fin && s == 1)
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goto start_fin;
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// Rabin >1
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else if (code.back().op != acc_cond::acc_op::Or)
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return nullptr;
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while (s)
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{
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--s;
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if (code[s].op == acc_cond::acc_op::And)
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{
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start_and:
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auto o1 = code[--s].op;
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auto m1 = code[--s].mark;
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auto o2 = code[--s].op;
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auto m2 = code[--s].mark;
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// We expect
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// Fin({n}) & Inf({n+1})
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if (o1 != acc_cond::acc_op::Fin ||
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o2 != acc_cond::acc_op::Inf ||
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m1.count() != 1 ||
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m2.count() != 1 ||
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m2 != (m1 << 1))
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return nullptr;
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inf_pairs |= m2;
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}
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else if (code[s].op == acc_cond::acc_op::Fin)
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{
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start_fin:
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fin_alone |= code[--s].mark;
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}
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else if (code[s].op == acc_cond::acc_op::Inf)
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{
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auto m1 = code[--s].mark;
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if (m1.count() != 1)
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return nullptr;
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inf_alone |= m1;
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}
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else
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{
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return nullptr;
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}
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}
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trace << "inf_pairs: " << inf_pairs << '\n';
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trace << "inf_alone: " << inf_alone << '\n';
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trace << "fin_alone: " << fin_alone << '\n';
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return ra_to_ba(aut, inf_pairs, inf_alone, fin_alone);
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}
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// If the DNF is
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// Fin(1)&Inf(2)&Inf(4) | Fin(2)&Fin(3)&Inf(1) |
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// Inf(1)&Inf(3) | Inf(1)&Inf(2) | Fin(4)
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@ -338,19 +449,19 @@ namespace spot
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}
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return res;
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}
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}
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twa_graph_ptr remove_fin(const const_twa_graph_ptr& aut)
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{
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auto maybe = streett_to_generalized_buchi_maybe(aut);
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if (maybe)
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return maybe;
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if (!aut->acc().uses_fin_acceptance())
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return std::const_pointer_cast<twa_graph>(aut);
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if (aut->has_state_based_acc() && aut->acc().is_rabin() > 0)
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return ra_to_ba(aut);
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if (auto maybe = streett_to_generalized_buchi_maybe(aut))
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return maybe;
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if (auto maybe = rabin_to_buchi_maybe(aut))
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return maybe;
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std::vector<acc_cond::acc_code> code;
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std::vector<acc_cond::mark_t> rem;
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