sat: skip reference transitions that are out of any cycle

* src/tgbaalgos/dtbasat.cc, src/tgbaalgos/dtgbasat.cc: Greatly reduce
the number of clauses and variable by removing any path variable that
reference a reference transition that is not in a SCC.

src/tgbaalgos/dtbasat.cc

@@ -217,10 +217,12 @@ namespace spot
       int size_;
       bdd ap_;
       bool state_based_;
+      scc_map& sm_;
     public:
-      filler_dfs(const tgba* aut, dict& d, bdd ap, bool state_based)
+      filler_dfs(const tgba* aut, dict& d, bdd ap, bool state_based,
+		 scc_map& sm)
 	: tgba_reachable_iterator_depth_first(aut), d(d), ap_(ap),
-	  state_based_(state_based)
+	  state_based_(state_based), sm_(sm)
       {
 	d.nvars = 0;
       }
@@ -237,14 +239,23 @@ namespace spot
 	if (d.cand_size == -1)
 	  d.cand_size = size_ - 1;
 
-	int seen_size = seen.size();
+	for (dict::state_map::const_iterator i2 = seen.begin();
-	for (int i = 1; i <= seen_size; ++i)
+	     i2 != seen.end(); ++i2)
 	  {
+	    int i = i2->second;
+	    d.int_to_state[i] = i2->first;
+	    unsigned i_scc = sm_.scc_of_state(i2->first);
+
 	    for (int j = 1; j <= d.cand_size; ++j)
 	      {
 		d.prodid[state_pair(j, i)] = ++d.nvars;
 
-		for (int k = 1; k <= seen_size; ++k)
+		for (dict::state_map::const_iterator k2 = seen.begin();
+		     k2 != seen.end(); ++k2)
+		  {
+		    int k = k2->second;
+		    if (sm_.scc_of_state(k2->first) != i_scc)
+		      continue;
 		    for (int l = 1; l <= d.cand_size; ++l)
 		    {
 		      path p(j, i, l, k);
@@ -253,11 +264,6 @@ namespace spot
 		    }
 		  }
 	      }
-
-	for (dict::state_map::const_iterator i = seen.begin();
-	     i != seen.end(); ++i)
-	  {
-	    d.int_to_state[i->second] = i->first;
 	  }
 
 	std::swap(d.state_to_int, seen);
@@ -314,7 +320,7 @@ namespace spot
 
       // Number all the SAT variable we may need.
       {
-	filler_dfs f(ref, d, ap, state_based);
+	filler_dfs f(ref, d, ap, state_based, sm);
 	f.run();
 	ref_size = f.size();
       }
@@ -450,11 +456,17 @@ namespace spot
       // construction of contraints (4,5) : all loops in the product
       // where no accepting run is detected in the ref. automaton,
       // must also be marked as not accepting in the cand. automaton
-      for (int q1 = 1; q1 <= d.cand_size; ++q1)
       for (int q1p = 1; q1p <= ref_size; ++q1p)
 	{
-	    for (int q2 = 1; q2 <= d.cand_size; ++q2)
+	  unsigned q1p_scc = sm.scc_of_state(d.int_to_state[q1p]);
 	  for (int q2p = 1; q2p <= ref_size; ++q2p)
+	    {
+	      // We are only interested in transition that can form a
+	      // cycle, so they must belong to the same SCC.
+	      if (sm.scc_of_state(d.int_to_state[q2p]) != q1p_scc)
+		continue;
+	      for (int q1 = 1; q1 <= d.cand_size; ++q1)
+		for (int q2 = 1; q2 <= d.cand_size; ++q2)
 		  {
 		    path p1(q1, q1p, q2, q2p);
 
@@ -463,12 +475,20 @@ namespace spot
 
 		    int pid1 = d.pathid_ref[p1];
 
-		  tgba_succ_iterator* it = ref->succ_iter(d.int_to_state[q2p]);
+		    tgba_succ_iterator* it =
+		      ref->succ_iter(d.int_to_state[q2p]);
 		    for (it->first(); !it->done(); it->next())
 		      {
 			const state* dps = it->current_state();
+			// Skip destinations not in the SCC.
+			if (sm.scc_of_state(dps) != q1p_scc)
+			  {
+			    dps->destroy();
+			    continue;
+			  }
 			int dp = d.state_to_int[dps];
 			dps->destroy();
+
 			if (it->current_acceptance_conditions() == all_acc)
 			  continue;
 			for (int q3 = 1; q3 <= d.cand_size; ++q3)
@@ -523,25 +543,38 @@ namespace spot
 		    delete it;
 		  }
 	    }
-
+	}
       // construction of contraints (6,7): all loops in the product
       // where accepting run is detected in the ref. automaton, must
       // also be marked as accepting in the candidate.
-      for (int q1 = 1; q1 <= d.cand_size; ++q1)
       for (int q1p = 1; q1p <= ref_size; ++q1p)
 	{
-	    for (int q2 = 1; q2 <= d.cand_size; ++q2)
+	  unsigned q1p_scc = sm.scc_of_state(d.int_to_state[q1p]);
 	  for (int q2p = 1; q2p <= ref_size; ++q2p)
+	    {
+	      // We are only interested in transition that can form a
+	      // cycle, so they must belong to the same SCC.
+	      if (sm.scc_of_state(d.int_to_state[q2p]) != q1p_scc)
+		continue;
+	      for (int q1 = 1; q1 <= d.cand_size; ++q1)
+		for (int q2 = 1; q2 <= d.cand_size; ++q2)
 		  {
 		    path p1(q1, q1p, q2, q2p);
 		    dout << "(6&7) matching paths from candidate based on "
 			 << p1 << "\n";
 		    int pid1 = d.pathid_cand[p1];
 
-		  tgba_succ_iterator* it = ref->succ_iter(d.int_to_state[q2p]);
+		    tgba_succ_iterator* it =
+		      ref->succ_iter(d.int_to_state[q2p]);
 		    for (it->first(); !it->done(); it->next())
 		      {
 			const state* dps = it->current_state();
+			// Skip destinations not in the SCC.
+			if (sm.scc_of_state(dps) != q1p_scc)
+			  {
+			    dps->destroy();
+			    continue;
+			  }
 			int dp = d.state_to_int[dps];
 			dps->destroy();
 			for (int q3 = 1; q3 <= d.cand_size; q3++)
@@ -601,7 +634,7 @@ namespace spot
 		    delete it;
 		  }
 	    }
-
+	}
       out.seekp(0);
       out << "p cnf " << d.nvars << " " << nclauses;
     }

src/tgbaalgos/dtgbasat.cc

@@ -298,10 +298,12 @@ namespace spot
       int size_;
       bdd ap_;
       bool state_based_;
+      scc_map& sm_;
     public:
-      filler_dfs(const tgba* aut, dict& d, bdd ap, bool state_based)
+      filler_dfs(const tgba* aut, dict& d, bdd ap, bool state_based,
+		 scc_map& sm)
 	: tgba_reachable_iterator_depth_first(aut), d(d), ap_(ap),
-	  state_based_(state_based)
+	  state_based_(state_based), sm_(sm)
       {
 	d.nvars = 0;
 
@@ -363,15 +365,22 @@ namespace spot
 	if (d.cand_size == -1)
 	  d.cand_size = size_ - 1;
 
-	int seen_size = seen.size();
+	for (dict::state_map::const_iterator i2 = seen.begin();
-	for (int i = 1; i <= seen_size; ++i)
+	     i2 != seen.end(); ++i2)
 	  {
+	    int i = i2->second;
+	    d.int_to_state[i] = i2->first;
+	    unsigned i_scc = sm_.scc_of_state(i2->first);
 	    for (int j = 1; j <= d.cand_size; ++j)
 	      {
 		d.prodid[state_pair(j, i)] = ++d.nvars;
 
-
+		for (dict::state_map::const_iterator k2 = seen.begin();
-		for (int k = 1; k <= seen_size; ++k)
+		     k2 != seen.end(); ++k2)
+		  {
+		    int k = k2->second;
+		    if (sm_.scc_of_state(k2->first) != i_scc)
+		      continue;
 		    for (int l = 1; l <= d.cand_size; ++l)
 		      {
 			size_t sf = d.all_cand_acc.size();
@@ -390,10 +399,7 @@ namespace spot
 		      }
 		  }
 	      }
-
+	  }
-	for (dict::state_map::const_iterator i = seen.begin();
-	     i != seen.end(); ++i)
-	  d.int_to_state[i->second] = i->first;
 
 	std::swap(d.state_to_int, seen);
 
@@ -491,7 +497,7 @@ namespace spot
 
       // Number all the SAT variable we may need.
       {
-	filler_dfs f(ref, d, ap, state_based);
+	filler_dfs f(ref, d, ap, state_based, sm);
 	f.run();
 	ref_size = f.size();
       }
@@ -623,10 +629,17 @@ namespace spot
       bdd all_acc = ref->all_acceptance_conditions();
 
       // construction of constraints (11,12,13)
-      for (int q1 = 1; q1 <= d.cand_size; ++q1)
       for (int q1p = 1; q1p <= ref_size; ++q1p)
-	  for (int q2 = 1; q2 <= d.cand_size; ++q2)
+	{
+	  unsigned q1p_scc = sm.scc_of_state(d.int_to_state[q1p]);
 	  for (int q2p = 1; q2p <= ref_size; ++q2p)
+	    {
+	      // We are only interested in transition that can form a
+	      // cycle, so they must belong to the same SCC.
+	      if (sm.scc_of_state(d.int_to_state[q2p]) != q1p_scc)
+		continue;
+	      for (int q1 = 1; q1 <= d.cand_size; ++q1)
+		for (int q2 = 1; q2 <= d.cand_size; ++q2)
 		  {
 		    size_t sf = d.all_cand_acc.size();
 		    size_t sfp = d.all_ref_acc.size();
@@ -646,13 +659,20 @@ namespace spot
 			  for (it->first(); !it->done(); it->next())
 			    {
 			      const state* dps = it->current_state();
+			      // Skip destinations not in the SCC.
+			      if (sm.scc_of_state(dps) != q1p_scc)
+				{
+				  dps->destroy();
+				  continue;
+				}
 			      int dp = d.state_to_int[dps];
 			      dps->destroy();
 
 			      for (int q3 = 1; q3 <= d.cand_size; ++q3)
 				{
 				  bdd all = it->current_condition();
-			      bdd curacc = it->current_acceptance_conditions();
+				  bdd curacc =
+				    it->current_acceptance_conditions();
 
 				  while (all != bddfalse)
 				    {
@@ -749,9 +769,6 @@ namespace spot
 						      << " " << tai << " 0\n";
 						  ++nclauses;
 						}
-					  // out << -pid << " " << -ti
-					  //     << " " << pcompid << " 0\n";
-					  // ++nclauses;
 					    }
 					}
 				      // (13) augmenting paths (always).
@@ -827,7 +844,8 @@ namespace spot
 			  delete it;
 			}
 		  }
-
+	    }
+	}
       out.seekp(0);
       out << "p cnf " << d.nvars << " " << nclauses;
     }