dtgbasat: add a colored option

This was suggested by one of the reviewers of our LPAR'15 paper.

* src/twaalgos/dtgbasat.cc, src/twaalgos/dtgbasat.hh: Implement
the colored option.
* src/tests/satmin2.test: Test it.
* doc/org/satmin.org, NEWS: Document it.

NEWS

@@ -1,6 +1,9 @@
 New in spot 1.99.3a (not yet released)
 
-  Nothing yet.
+  * autfilt's --sat-minimize now takes a "colored" option to constrain
+    all transitions (or states) in the output automaton to belong to
+    exactly one acceptance sets.  This is useful when targeting parity
+    acceptance.
 
 New in spot 1.99.3 (2015-08-26)
 

doc/org/satmin.org

@@ -35,10 +35,10 @@ Let us first state a few facts about this minimization procedure.
    to the SAT solver) exceeds $2^{31}$, or when the SAT-solver was
    killed by a signal. [[file:autfilt.org][=autfilt --sat-minimize=]] will only output an
    automaton if the SAT-based minimization was successful.
-6) Our [[https://www.lrde.epita.fr/~adl/dl/adl/baarir.14.forte.pdf%0A][FORTE'14 paper]] describes the SAT encoding for the minimization
-   of deterministic BA and TGBA.  Since then, the technique used in
-   the SAT encoding for deterministic TGBA has been generalized to
-   deal with any deterministic TωA.
+6) Our [[https://www.lrde.epita.fr/~adl/dl/adl/baarir.14.forte.pdf][FORTE'14 paper]] describes the SAT encoding for the minimization
+   of deterministic BA and TGBA.  Our [[https://www.lrde.epita.fr/~adl/dl/adl/baarir.15.lpar.pdf][LPAR'15 paper]] describes the
+   generalization of the SAT encoding to deal with deterministic TωA
+   with any acceptance condition.
 
 * How to change the SAT solver used
 
@@ -672,6 +672,91 @@ that can be any of the following:
 - =dichotomy= :: instead of looking for a smaller automaton starting
      from =N=, and then checking =N-1=, =N-2=, etc., do a binary
      search starting from =N/2=.
+- =colored= :: force all transitions (or all states if =-S= is used)
+     to belong to exactly one acceptance condition.
+
+
+The =colored= option is useful when used in conjunction with a parity
+acceptance condition.  Indeed, the parity acceptance condition by
+itself does not require that the acceptance sets form a partition of
+the automaton (which is expected from parity automata).
+
+Compare the following, where parity acceptance is used, but the
+automaton is not colored:
+
+#+NAME: autfiltsm9
+#+BEGIN_SRC sh :results verbatim :exports code
+autfilt -S --sat-minimize='acc="parity max even 3"' output2.hoa --dot=.a
+#+END_SRC
+#+RESULTS: autfiltsm9
+#+begin_example
+digraph G {
+  rankdir=LR
+  label=<Inf(<font color="#FAA43A">❷</font>) | (Fin(<font color="#F17CB0">❶</font>) &amp; Inf(<font color="#5DA5DA">⓿</font>))>
+  labelloc="t"
+  node [shape="circle"]
+  fontname="Lato"
+  node [fontname="Lato"]
+  edge [fontname="Lato"]
+  node[style=filled, fillcolor="#ffffa0"] edge[arrowhead=vee, arrowsize=.7]
+  I [label="", style=invis, width=0]
+  I -> 0
+  0 [label=<0>]
+  0 -> 0 [label=<!a>]
+  0 -> 1 [label=<a &amp; !b>]
+  0 -> 2 [label=<a &amp; b>]
+  1 [label=<1>]
+  1 -> 1 [label=<!b>]
+  1 -> 2 [label=<b>]
+  2 [label=<2<br/><font color="#5DA5DA">⓿</font>>]
+  2 -> 0 [label=<1>]
+}
+#+end_example
+
+#+BEGIN_SRC dot :file autfiltsm9.png :cmdline -Tpng :var txt=autfiltsm9 :exports results
+$txt
+#+END_SRC
+
+#+RESULTS:
+[[file:autfiltsm9.png]]
+
+... to the following, where the automaton is colored, i.e., each state
+belong to exactly one acceptance set:
+
+#+NAME: autfiltsm10
+#+BEGIN_SRC sh :results verbatim :exports code
+autfilt -S --sat-minimize='acc="parity max even 3",colored' output2.hoa --dot=.a
+#+END_SRC
+#+RESULTS: autfiltsm10
+#+begin_example
+digraph G {
+  rankdir=LR
+  label=<Inf(<font color="#FAA43A">❷</font>) | (Fin(<font color="#F17CB0">❶</font>) &amp; Inf(<font color="#5DA5DA">⓿</font>))>
+  labelloc="t"
+  node [shape="circle"]
+  fontname="Lato"
+  node [fontname="Lato"]
+  edge [fontname="Lato"]
+  node[style=filled, fillcolor="#ffffa0"] edge[arrowhead=vee, arrowsize=.7]
+  I [label="", style=invis, width=0]
+  I -> 0
+  0 [label=<0<br/><font color="#F17CB0">❶</font>>]
+  0 -> 0 [label=<!b>]
+  0 -> 1 [label=<b>]
+  1 [label=<1<br/><font color="#F17CB0">❶</font>>]
+  1 -> 1 [label=<!a>]
+  1 -> 2 [label=<a>]
+  2 [label=<2<br/><font color="#FAA43A">❷</font>>]
+  2 -> 0 [label=<1>]
+}
+#+end_example
+
+#+BEGIN_SRC dot :file autfiltsm10.png :cmdline -Tpng :var txt=autfiltsm10 :exports results
+$txt
+#+END_SRC
+
+#+RESULTS:
+[[file:autfiltsm10.png]]
 
 * Logging statistics
 

src/tests/satmin2.test

@@ -112,6 +112,15 @@ $autfilt -S --sat-minimize='acc="Fin(0)|Inf(1)"' test.hoa \
 	 --stats=%s > output
 test `cat output` = 3
 
+# How about a state-based DPA?
+$autfilt -S --sat-minimize='acc="parity max even 3",colored' -H test.hoa \
+	 > output
+cat output
+grep 'properties:.*colored' output
+grep 'States: 3' output
+grep 'acc-name: parity max even 3' output
+grep 'Acceptance: 3 Inf(2) | (Fin(1) & Inf(0))' output
+test 3 = `grep -c 'State: [012] {[012]}' output`
 
 # I get headaches whenever I think about this acceptance condition, so
 # it should be a good test case.

src/twaalgos/dtgbasat.cc

@@ -604,7 +604,7 @@ namespace spot
 
     static
     sat_stats dtgba_to_sat(std::ostream& out, const_twa_graph_ptr ref,
-			   dict& d, bool state_based)
+			   dict& d, bool state_based, bool colored)
     {
 #if DEBUG
       debug_dict = ref->get_dict();
@@ -714,6 +714,45 @@ namespace spot
 	++nclauses;
       }
 
+      if (colored)
+	{
+	  unsigned nacc = d.cand_nacc;
+	  dout << "transitions belong to exactly one of the "
+	       << nacc << " acceptance set\n";
+	  bdd all = bddtrue;
+	  while (all != bddfalse)
+	    {
+	      bdd l = bdd_satoneset(all, ap, bddfalse);
+	      all -= l;
+	      for (unsigned q1 = 0; q1 < d.cand_size; ++q1)
+		for (unsigned q2 = 0; q2 < d.cand_size; ++q2)
+		  {
+		    for (unsigned i = 0; i < nacc; ++i)
+		      {
+			transition_acc ti(q1, l, {i}, q2);
+			int tai = d.transaccid[ti];
+
+			for (unsigned j = 0; j < nacc; ++j)
+			  if (i != j)
+			    {
+			      transition_acc tj(q1, l, {j}, q2);
+			      int taj = d.transaccid[tj];
+			      out << -tai << ' ' << -taj << " 0\n";
+			      ++nclauses;
+			    }
+		      }
+		    for (unsigned i = 0; i < nacc; ++i)
+		      {
+			transition_acc ti(q1, l, {i}, q2);
+			int tai = d.transaccid[ti];
+			out << tai << ' ';
+		      }
+		    out << "0\n";
+		    ++nclauses;
+		  }
+	    }
+	}
+
       if (!d.all_silly_cand_acc.empty())
 	{
 	  dout << "no transition with silly acceptance\n";
@@ -1084,7 +1123,8 @@ namespace spot
   dtgba_sat_synthetize(const const_twa_graph_ptr& a,
 		       unsigned target_acc_number,
 		       const acc_cond::acc_code& target_acc,
-		       int target_state_number, bool state_based)
+		       int target_state_number,
+		       bool state_based, bool colored)
   {
     if (target_state_number == 0)
       return nullptr;
@@ -1103,7 +1143,7 @@ namespace spot
 
     timer_map t;
     t.start("encode");
-    sat_stats s = dtgba_to_sat(solver(), a, d, state_based);
+    sat_stats s = dtgba_to_sat(solver(), a, d, state_based, colored);
     t.stop("encode");
     t.start("solve");
     solution = solver.get_solution();
@@ -1156,8 +1196,8 @@ namespace spot
   dtgba_sat_minimize(const const_twa_graph_ptr& a,
 		     unsigned target_acc_number,
 		     const acc_cond::acc_code& target_acc,
-		     bool state_based,
-		     int max_states)
+		     bool state_based, int max_states,
+		     bool colored)
   {
     int n_states = (max_states < 0) ?
       stats_reachable(a).states : max_states + 1;
@@ -1167,7 +1207,8 @@ namespace spot
       {
 	auto next =
 	  dtgba_sat_synthetize(prev ? prev : a, target_acc_number,
-			       target_acc, --n_states, state_based);
+			       target_acc, --n_states,
+			       state_based, colored);
 	if (!next)
 	  return prev;
 	else
@@ -1181,8 +1222,8 @@ namespace spot
   dtgba_sat_minimize_dichotomy(const const_twa_graph_ptr& a,
 			       unsigned target_acc_number,
 			       const acc_cond::acc_code& target_acc,
-			       bool state_based,
-			       int max_states)
+			       bool state_based, int max_states,
+			       bool colored)
   {
     if (max_states < 1)
       max_states = stats_reachable(a).states - 1;
@@ -1194,7 +1235,8 @@ namespace spot
 	int target = (max_states + min_states) / 2;
 	auto next =
 	  dtgba_sat_synthetize(prev ? prev : a, target_acc_number,
-			       target_acc, target, state_based);
+			       target_acc, target, state_based,
+			       colored);
 	if (!next)
 	  {
 	    min_states = target + 1;
@@ -1228,6 +1270,7 @@ namespace spot
     int states = om.get("states", -1);
     int max_states = om.get("max-states", -1);
     auto accstr = om.get_str("acc");
+    bool colored = om.get("colored", 0);
 
     // Assume we are going to use the input automaton acceptance...
     bool user_supplied_acc = false;
@@ -1316,9 +1359,9 @@ namespace spot
     if (states == -1)
       {
 	auto orig = a;
-	if (!target_is_buchi || !a->acc().is_buchi())
+	if (!target_is_buchi || !a->acc().is_buchi() || colored)
 	  a = (dicho ? dtgba_sat_minimize_dichotomy : dtgba_sat_minimize)
-	    (a, nacc, target_acc, state_based, max_states);
+	    (a, nacc, target_acc, state_based, max_states, colored);
 	else
 	  a = (dicho ? dtba_sat_minimize_dichotomy : dtba_sat_minimize)
 	    (a, state_based, max_states);
@@ -1328,8 +1371,9 @@ namespace spot
       }
     else
       {
-	if (!target_is_buchi || !a->acc().is_buchi())
-	  a = dtgba_sat_synthetize(a, nacc, target_acc, states, state_based);
+	if (!target_is_buchi || !a->acc().is_buchi() || colored)
+	  a = dtgba_sat_synthetize(a, nacc, target_acc, states,
+				   state_based, colored);
 	else
 	  a = dtba_sat_synthetize(a, states, state_based);
       }

src/twaalgos/dtgbasat.hh

@@ -41,6 +41,9 @@ namespace spot
   /// of a state to share the same acceptance conditions, effectively
   /// turning the TGBA into a TBA.
   ///
+  /// \param colored if true, force all transitions to belong to
+  /// exactly one acceptance set.
+  ///
   /// This functions attempts to find a TGBA with \a target_acc_number
   /// acceptance sets and target_state_number states that is
   /// equivalent to \a a.  If no such TGBA is found, a null pointer is
@@ -50,7 +53,8 @@ namespace spot
 		       unsigned target_acc_number,
 		       const acc_cond::acc_code& target_acc,
 		       int target_state_number,
-		       bool state_based = false);
+		       bool state_based = false,
+		       bool colored = false);
 
   /// \brief Attempt to minimize a deterministic TGBA with a SAT solver.
   ///
@@ -63,7 +67,8 @@ namespace spot
 		     unsigned target_acc_number,
 		     const acc_cond::acc_code& target_acc,
 		     bool state_based = false,
-		     int max_states = -1);
+		     int max_states = -1,
+		     bool colored = false);
 
   /// \brief Attempt to minimize a deterministic TGBA with a SAT solver.
   ///
@@ -76,7 +81,8 @@ namespace spot
 			       unsigned target_acc_number,
 			       const acc_cond::acc_code& target_acc,
 			       bool state_based = false,
-			       int max_states = -1);
+			       int max_states = -1,
+			       bool colored = false);
 
   /// \brief High-level interface to SAT-based minimization
   ///
@@ -90,6 +96,7 @@ namespace spot
   ///   acc = "Rabin 3"
   ///   acc = "same" /* default */
   ///   dichotomy = 1    // use dichotomy instead of decreasing loop
+  ///   colored = 1      // build a colored TωA
   ///
   SPOT_API twa_graph_ptr
   sat_minimize(twa_graph_ptr aut, const char* opt, bool state_based = false);