Add a notebook illustrating decompose_strength()

* wrap/python/tests/decompose.ipynb: New file.
* wrap/python/tests/Makefile.am: Add it.
* src/twaalgos/strength.cc: Fix corner cases.
* src/tests/strength.test: Adjust corner case.
* NEWS, doc/org/tut.org: Mention the notebook.

NEWS

@@ -6,6 +6,8 @@ New in spot 1.99.5a (not yet released)
 
   * autfilt has a new transformation: --decompose-strength,
     implementing the decomposition of our TACAS'13 paper.
+    A demonstration of this feature via the Python bindings
+    can be found at https://spot.lrde.epita.fr/ipynb/decompose.html
 
   * All tools that output HOA files accept a --check=strength option
     to request automata to be marked as "weak" or "terminal" as

doc/org/tut.org

@@ -54,5 +54,6 @@ real notebooks instead.
   after acceptance simplification
 - [[https://spot.lrde.epita.fr/ipynb/accparse.html][accparse.ipynb]] exercises the acceptance condition parser
 - [[https://spot.lrde.epita.fr/ipynb/randltl.html][randltl.ipynb]] demonstrates a Python-version of [[file:randltl.org][=randltl=]]
+- [[https://spot.lrde.epita.fr/ipynb/decompose.html][decompose.ipynb]] illustrates the =decompose_strength()= function
 - [[https://spot.lrde.epita.fr/ipynb/testingaut.html][testingaut.ipynb]] shows the step necessary to build a testing
   automaton

src/tests/strength.test

@@ -535,14 +535,14 @@ HOA: v1
 States: 2
 Start: 0
 AP: 0
-acc-name: all
-Acceptance: 0 t
-properties: trans-labels explicit-labels state-acc complete
+acc-name: Buchi
+Acceptance: 1 Inf(0)
+properties: trans-labels explicit-labels state-acc colored complete
 properties: deterministic weak
 --BODY--
-State: 0
+State: 0 {0}
 [t] 1
-State: 1
+State: 1 {0}
 [t] 0
 --END--
 HOA: v1

src/twaalgos/strength.cc

@@ -148,6 +148,33 @@ namespace spot
 	    (std::string("unknown option for decompose_strength(): ") + c);
 	}
 
+    acc_cond::mark_t wacc = 0U;	// Acceptance for weak SCCs
+    acc_cond::mark_t uacc = 0U;	// Acceptance for "needed" SCCs, that
+				// we only want to traverse.
+
+    // If the acceptance condition is always satisfiable, we will
+    // consider the automaton has weak (even if that is not the
+    // case syntactically) and not output any strong part.
+    bool all_accepting = false;
+    if (aut->acc().is_tt())
+      {
+	all_accepting = true;
+      }
+    else if (aut->acc().uses_fin_acceptance())
+      {
+	auto p = aut->get_acceptance().unsat_mark();
+	if (p.first)
+	  uacc = p.second;
+	else
+	  all_accepting = true;
+      }
+    if (all_accepting)
+      {
+	keep &= ~Strong;
+	if (keep == Ignore)
+	  return nullptr;
+      }
+
     scc_info si(aut);
     si.determine_unknown_acceptance();
 
@@ -160,7 +187,7 @@ namespace spot
       {
 	if (si.is_accepting_scc(i))
 	  {
-	    if (is_weak_scc(si, i))
+	    if (all_accepting | is_weak_scc(si, i))
 	      {
 		if (keep & Weak)
 		  {
@@ -194,23 +221,10 @@ namespace spot
     res->copy_ap_of(aut);
     res->prop_copy(aut, { true, false, true, false });
 
-    acc_cond::mark_t wacc = 0U;	// Acceptance for weak SCCs
-    acc_cond::mark_t uacc = 0U;	// Acceptance for "needed" SCCs, that
-				// we only want to traverse.
     if (keep & Strong)
-      {
-	res->copy_acceptance_of(aut);
-	auto& ac = res->acc();
-	if (ac.uses_fin_acceptance())
-	  // Note that we ignore the cases where the acceptance
-	  // condition is always satisfiable.  In that case
-	  // uacc will be set to 0U, which will be satisfiable
-	  uacc = ac.get_acceptance().unsat_mark().second;
-      }
+      res->copy_acceptance_of(aut);
     else
-      {
-	wacc = res->set_buchi();
-      }
+      wacc = res->set_buchi();
 
     auto fun = [&si, &want, uacc, wacc, keep]
       (unsigned src, bdd& cond, acc_cond::mark_t& acc, unsigned dst)

wrap/python/tests/Makefile.am

@@ -37,6 +37,7 @@ TESTS = \
   automata.ipynb \
   automata-io.ipynb \
   bddnqueen.py \
+  decompose.ipynb \
   formulas.ipynb \
   implies.py \
   interdep.py \