translate: enable a restricted form of ltl-split for TGBA/BA

Fixes #267 * spot/twaalgos/gfguarantee.cc: Fix a typo when comparing automata sizes. * spot/twaalgos/translate.cc, spot/twaalgos/translate.hh: Use ltl-split even for BA/TGBA, but only of conjunctions with GF(..) in those cases. * tests/core/ltl2tgba2.test: Adjust and add the example of #267. * tests/core/degenid.test, tests/core/parity2.test, tests/core/stutter-tgba.test, tests/python/automata.ipynb, tests/python/highlighting.ipynb, tests/python/stutter-inv.ipynb, bin/spot-x.cc: Adjust.
2018-06-28 23:02:26 +02:00 · 2018-06-28 23:02:26 +02:00 · f5f5daec9a
commit f5f5daec9a
parent 4235b007f3
11 changed files with 1338 additions and 1494 deletions
--- a/bin/spot-x.cc
+++ b/bin/spot-x.cc
@ -46,8 +46,7 @@ more rules based on automata-based implication checks.  The default value \
 depends on the --low/--medium/--high settings.") },
    { nullptr, 0, nullptr, 0, "Translation options:", 0 },
    { DOC("ltl-split", "Set to 0 to disable the translation of automata \
-as product or sum of subformulas.  This is currently used only when \
-building automata with generic acceptance conditions.") },
+as product or sum of subformulas.") },
    { DOC("comp-susp", "Set to 1 to enable compositional suspension, \
 as described in our SPIN'13 paper (see Bibliography below).  Set to 2, \
 to build only the skeleton TGBA without composing it.  Set to 0 (the \
--- a/spot/twaalgos/gfguarantee.cc
+++ b/spot/twaalgos/gfguarantee.cc
@ -418,7 +418,7 @@ namespace spot
        if (!is_terminal_automaton(aut, &si2, true))
          return reduced;
        do_g_f_terminal_inplace(si2, state_based);
-        if (aut->num_states() <= reduced->num_states())
+        if (aut->num_states() < reduced->num_states())
          return aut;
      }
    return reduced;
--- a/spot/twaalgos/translate.cc
+++ b/spot/twaalgos/translate.cc
@ -105,7 +105,8 @@ namespace spot
    simpl_owned_ = simpl_ = new tl_simplifier(options, dict);
  }

-  twa_graph_ptr translator::run(formula* f)
+
+  twa_graph_ptr translator::run_aux(formula r)
  {
 #define PREF_ (pref_ & (Small | Deterministic))

@ -118,49 +119,6 @@ namespace spot
        set_pref(pref_ | postprocessor::Deterministic);
      }

-    // Do we want to relabel Boolean subformulas?
-    // If we have a huge formula such as
-    //  (a1 & a2 & ... & an) U (b1 | b2 | ... | bm)
-    // then it is more efficient to translate
-    //  a U b
-    // and then fix the automaton.  We use relabel_bse() to find
-    // sub-formulas that are Boolean but do not have common terms.
-    //
-    // This rewriting is enabled only if the formula
-    //  1) has some Boolean subformula
-    //  2) has more than relabel_bool_ atomic propositions (the default
-    //     is 4, but this can be changed)
-    //  3) relabel_bse() actually reduces the number of atomic
-    //     propositions.
-    relabeling_map m;
-    formula to_work_on = *f;
-    if (relabel_bool_ > 0)
-      {
-        bool has_boolean_sub = false; // that is not atomic
-        std::set<formula> aps;
-        to_work_on.traverse([&](const formula& f)
-                            {
-                              if (f.is(op::ap))
-                                aps.insert(f);
-                              else if (f.is_boolean())
-                                has_boolean_sub = true;
-                              return false;
-                            });
-        unsigned atomic_props = aps.size();
-        if (has_boolean_sub && (atomic_props >= (unsigned) relabel_bool_))
-          {
-            formula relabeled = relabel_bse(to_work_on, Pnn, &m);
-            if (m.size() < atomic_props)
-              to_work_on = relabeled;
-            else
-              m.clear();
-          }
-      }
-
-    formula r = simpl_->simplify(to_work_on);
-    if (to_work_on == *f)
-      *f = r;
-
    // This helps ltl_to_tgba_fm() to order BDD variables in a more
    // natural way (improving the degeneralization).
    simpl_->clear_as_bdd_cache();
@ -168,8 +126,7 @@ namespace spot
    twa_graph_ptr aut;
    twa_graph_ptr aut2 = nullptr;

-    if (ltl_split_ && (type_ == Generic
-                       || (type_ & Parity)) && !r.is_syntactic_obligation())
+    if (ltl_split_ && !r.is_syntactic_obligation())
      {
        formula r2 = r;
        unsigned leading_x = 0;
@ -178,11 +135,11 @@ namespace spot
            r2 = r2[0];
            ++leading_x;
          }
-        if (type_ == Generic)
+        if (type_ == Generic || type_ == TGBA)
          {
-            // F(q|u|f) = q|F(u)|F(f)
+            // F(q|u|f) = q|F(u)|F(f)  only for generic acceptance
            // G(q&e&f) = q&G(e)&G(f)
-            bool want_u = r2.is({op::F, op::Or});
+            bool want_u = r2.is({op::F, op::Or}) && (type_ == Generic);
            if (want_u || r2.is({op::G, op::And}))
              {
                std::vector<formula> susp;
@ -204,7 +161,12 @@ namespace spot
                r2 = formula::multop(op2, susp);
              }
          }
-        if (r2.is_syntactic_obligation() || !r2.is(op::And, op::Or))
+        if (r2.is_syntactic_obligation() || !r2.is(op::And, op::Or) ||
+            // For TGBA/BA we only do conjunction.  There is nothing wrong
+            // with disjunction, but it seems to generated larger automata
+            // in many cases and it needs to be further investigated.  Maybe
+            // this could be relaxed in the case of deterministic output.
+            (r2.is(op::Or) && (type_ == TGBA || type_ == BA)))
          goto nosplit;

        bool is_and = r2.is(op::And);
@ -212,16 +174,38 @@ namespace spot
        std::vector<formula> oblg;
        std::vector<formula> susp;
        std::vector<formula> rest;
+        bool want_g = type_ == TGBA || type_ == BA;
        for (formula child: r2)
          {
            if (child.is_syntactic_obligation())
              oblg.push_back(child);
            else if (child.is_eventual() && child.is_universal()
-                     && (type_ == Generic))
+                     && (!want_g || child.is(op::G)))
              susp.push_back(child);
            else
              rest.push_back(child);
          }
+
+        if (!susp.empty())
+          {
+            // The only cases where we accept susp and rest to be both
+            // non-empty is when doing arbitrary acceptance, or when doing
+            // Generic or TGBA.
+            if (!rest.empty() && !(type_ == Generic || type_ == TGBA))
+              {
+                rest.insert(rest.end(), susp.begin(), susp.end());
+                susp.clear();
+              }
+            // For Parity, we want to translate all suspendable
+            // formulas at once.
+            if (rest.empty() && type_ & Parity)
+              susp = { formula::multop(r2.kind(), susp) };
+          }
+        // For TGBA and BA, we only split if there is something to
+        // suspend.
+        if (susp.empty() && (type_ == TGBA || type_ == BA))
+          goto nosplit;
+
        option_map om;
        if (opt_)
          om = *opt_;
@ -238,34 +222,26 @@ namespace spot
              return run(f);
          };

+        // std::cerr << "splitting\n";
        aut = nullptr;
        // All obligations can be converted into a minimal WDBA.
        if (!oblg.empty())
          {
            formula oblg_f = formula::multop(r2.kind(), oblg);
+            //std::cerr << "oblg: " << oblg_f << '\n';
            aut = transrun(oblg_f);
          }
        if (!rest.empty())
          {
            formula rest_f = formula::multop(r2.kind(), rest);
-            // In case type_ is Parity, all suspendable formulas have
-            // been put into rest_f.  But if the entire rest_f is
-            // suspendable, we want to handle it like so.
-            if (rest_f.is_eventual() && rest_f.is_universal())
-              {
-                assert(susp.empty());
-                susp.push_back(rest_f);
-              }
+            //std::cerr << "rest: " << rest_f << '\n';
+            twa_graph_ptr rest_aut = transrun(rest_f);
+            if (aut == nullptr)
+              aut = rest_aut;
+            else if (is_and)
+              aut = product(aut, rest_aut);
            else
-              {
-                twa_graph_ptr rest_aut = transrun(rest_f);
-                if (aut == nullptr)
-                  aut = rest_aut;
-                else if (is_and)
-                  aut = product(aut, rest_aut);
-                else
-                  aut = product_or(aut, rest_aut);
-              }
+              aut = product_or(aut, rest_aut);
          }
        if (!susp.empty())
          {
@ -273,6 +249,7 @@ namespace spot
            // Each suspendable formula separately
            for (formula f: susp)
              {
+                //std::cerr << "susp: " << f << '\n';
                twa_graph_ptr one = transrun(f);
                if (!susp_aut)
                  susp_aut = one;
@ -370,6 +347,56 @@ namespace spot
          aut = std::move(aut2);
      }

+    return aut;
+  }
+
+  twa_graph_ptr translator::run(formula* f)
+  {
+    // Do we want to relabel Boolean subformulas?
+    // If we have a huge formula such as
+    //  (a1 & a2 & ... & an) U (b1 | b2 | ... | bm)
+    // then it is more efficient to translate
+    //  a U b
+    // and then fix the automaton.  We use relabel_bse() to find
+    // sub-formulas that are Boolean but do not have common terms.
+    //
+    // This rewriting is enabled only if the formula
+    //  1) has some Boolean subformula
+    //  2) has more than relabel_bool_ atomic propositions (the default
+    //     is 4, but this can be changed)
+    //  3) relabel_bse() actually reduces the number of atomic
+    //     propositions.
+    relabeling_map m;
+    formula to_work_on = *f;
+    if (relabel_bool_ > 0)
+      {
+        bool has_boolean_sub = false; // that is not atomic
+        std::set<formula> aps;
+        to_work_on.traverse([&](const formula& f)
+                            {
+                              if (f.is(op::ap))
+                                aps.insert(f);
+                              else if (f.is_boolean())
+                                has_boolean_sub = true;
+                              return false;
+                            });
+        unsigned atomic_props = aps.size();
+        if (has_boolean_sub && (atomic_props >= (unsigned) relabel_bool_))
+          {
+            formula relabeled = relabel_bse(to_work_on, Pnn, &m);
+            if (m.size() < atomic_props)
+              to_work_on = relabeled;
+            else
+              m.clear();
+          }
+      }
+
+    formula r = simpl_->simplify(to_work_on);
+    if (to_work_on == *f)
+      *f = r;
+
+    auto aut = run_aux(r);
+
    if (!m.empty())
      relabel_here(aut, &m);
    return aut;
--- a/spot/twaalgos/translate.hh
+++ b/spot/twaalgos/translate.hh
@ -138,6 +138,7 @@ namespace spot
  protected:
    void setup_opt(const option_map* opt);
    void build_simplifier(const bdd_dict_ptr& dict);
+    twa_graph_ptr run_aux(formula f);

  private:
    tl_simplifier* simpl_;
--- a/tests/core/degenid.test
+++ b/tests/core/degenid.test
@ -1,7 +1,7 @@
 #!/bin/sh
 # -*- coding: utf-8 -*-
-# Copyright (C) 2011, 2013, 2014, 2015, 2017 Laboratoire de Recherche
-# et Développement de l'Epita (LRDE).
+# Copyright (C) 2011, 2013, 2014, 2015, 2017, 2018 Laboratoire de
+# Recherche et Développement de l'Epita (LRDE).
 #
 # This file is part of Spot, a model checking library.
 #
@ -239,7 +239,9 @@ properties: trans-labels explicit-labels state-acc deterministic
 properties: stutter-invariant
 --BODY--
 State: 0
-[0] 1
+[0&1&2] 1
+[0&!2] 2
+[0&!1&2] 3
 State: 1 {0}
 [1&2] 1
 [!2] 2
--- a/tests/core/ltl2tgba2.test
+++ b/tests/core/ltl2tgba2.test
@ -362,12 +362,14 @@ EOF
 diff output expected


-# These four formulas appear in a NEWS entry for Spot 2.6
+# The first four formulas appear in a NEWS entry for Spot 2.6
+# The 5th one is from issue #267.
 cat >formulas <<EOF
 GF((a & XXa) | (!a & XX!a)), 4,8, 4,8, 6,14, 7,14
 GF((a & XXXa) | (!a & XXX!a)), 7,14, 8,16, 8,18, 15,30
-GF(((a & Xb) | XXc) & Xd), 4,60, 4,64, 4,68, 5,80
+GF(((a & Xb) | XXc) & Xd), 4,64, 4,64, 5,80, 5,80
 GF((b | Fa) & (b R Xb)), 2,4, 2,4, 3,6, 3,12
+G(F(a & Xa) & F(a & X!a)), 2,4, 2,4, 4,8, 4,8
 EOF

 ltl2tgba -Fformulas/1 --stats='%f, %s,%t' |
--- a/tests/core/parity2.test
+++ b/tests/core/parity2.test
@ -426,7 +426,7 @@ State: 1
 --END--
 HOA: v1
 name: "(p0 W XXGp0) & G(Fp1 & FGp2)"
-States: 6
+States: 5
 Start: 0
 AP: 3 "p0" "p1" "p2"
 acc-name: Buchi
@ -435,23 +435,21 @@ properties: trans-labels explicit-labels trans-acc
 --BODY--
 State: 0
 [0] 0
-[t] 2
-[0&1&2] 3
+[!0] 1
+[0&1&2] 2
 State: 1
-[2] 4
-State: 2
+[t] 3
 [1&2] 4
-[t] 5
+State: 2
+[!0] 1
+[0&!1&2] 2
+[0&1&2] 2 {0}
 State: 3
-[2] 1
-[0&!1&2] 3
-[0&1&2] 3 {0}
+[0] 3
+[0&1&2] 4
 State: 4
 [0&!1&2] 4
 [0&1&2] 4 {0}
-State: 5
-[0&1&2] 4
-[0] 5
 --END--
 HOA: v1
 name: "FGa"
@ -489,7 +487,7 @@ State: 1
 --END--
 HOA: v1
 name: "(p0 W XXGp0) & G(Fp1 & FGp2)"
-States: 6
+States: 5
 Start: 0
 AP: 3 "p0" "p1" "p2"
 acc-name: Rabin 1
@ -498,23 +496,21 @@ properties: trans-labels explicit-labels trans-acc
 --BODY--
 State: 0
 [0] 0
-[t] 2
-[0&1&2] 3
+[!0] 1
+[0&1&2] 2
 State: 1
-[2] 4
-State: 2
+[t] 3
 [1&2] 4
-[t] 5
+State: 2
+[!0] 1
+[0&!1&2] 2
+[0&1&2] 2 {1}
 State: 3
-[2] 1
-[0&!1&2] 3
-[0&1&2] 3 {1}
+[0] 3
+[0&1&2] 4
 State: 4
 [0&!1&2] 4
 [0&1&2] 4 {1}
-State: 5
-[0&1&2] 4
-[0] 5
 --END--
 HOA: v1
 name: "FGa"
@ -552,7 +548,7 @@ State: 1
 --END--
 HOA: v1
 name: "(p0 W XXGp0) & G(Fp1 & FGp2)"
-States: 6
+States: 5
 Start: 0
 AP: 3 "p0" "p1" "p2"
 acc-name: Buchi
@ -561,23 +557,21 @@ properties: trans-labels explicit-labels trans-acc
 --BODY--
 State: 0
 [0] 0
-[t] 2
-[0&1&2] 3
+[!0] 1
+[0&1&2] 2
 State: 1
-[2] 4
-State: 2
+[t] 3
 [1&2] 4
-[t] 5
+State: 2
+[!0] 1
+[0&!1&2] 2
+[0&1&2] 2 {0}
 State: 3
-[2] 1
-[0&!1&2] 3
-[0&1&2] 3 {0}
+[0] 3
+[0&1&2] 4
 State: 4
 [0&!1&2] 4
 [0&1&2] 4 {0}
-State: 5
-[0&1&2] 4
-[0] 5
 --END--
 HOA: v1
 name: "FGa"
@ -615,7 +609,7 @@ State: 1
 --END--
 HOA: v1
 name: "(p0 W XXGp0) & G(Fp1 & FGp2)"
-States: 6
+States: 5
 Start: 0
 AP: 3 "p0" "p1" "p2"
 acc-name: Streett 1
@ -624,23 +618,21 @@ properties: trans-labels explicit-labels trans-acc colored
 --BODY--
 State: 0
 [0] 0 {0}
-[t] 2 {0}
-[0&1&2] 3 {0}
+[!0] 1 {0}
+[0&1&2] 2 {0}
 State: 1
-[2] 4 {0}
-State: 2
+[t] 3 {0}
 [1&2] 4 {0}
-[t] 5 {0}
+State: 2
+[!0] 1 {0}
+[0&!1&2] 2 {0}
+[0&1&2] 2 {1}
 State: 3
-[2] 1 {0}
-[0&!1&2] 3 {0}
-[0&1&2] 3 {1}
+[0] 3 {0}
+[0&1&2] 4 {0}
 State: 4
 [0&!1&2] 4 {0}
 [0&1&2] 4 {1}
-State: 5
-[0&1&2] 4 {0}
-[0] 5 {0}
 --END--
 HOA: v1
 name: "FGa"
@ -678,7 +670,7 @@ State: 1
 --END--
 HOA: v1
 name: "(p0 W XXGp0) & G(Fp1 & FGp2)"
-States: 6
+States: 5
 Start: 0
 AP: 3 "p0" "p1" "p2"
 acc-name: parity min odd 3
@ -687,23 +679,21 @@ properties: trans-labels explicit-labels trans-acc colored
 --BODY--
 State: 0
 [0] 0 {2}
-[t] 2 {2}
-[0&1&2] 3 {2}
+[!0] 1 {2}
+[0&1&2] 2 {2}
 State: 1
-[2] 4 {2}
-State: 2
+[t] 3 {2}
 [1&2] 4 {2}
-[t] 5 {2}
+State: 2
+[!0] 1 {2}
+[0&!1&2] 2 {2}
+[0&1&2] 2 {1}
 State: 3
-[2] 1 {2}
-[0&!1&2] 3 {2}
-[0&1&2] 3 {1}
+[0] 3 {2}
+[0&1&2] 4 {2}
 State: 4
 [0&!1&2] 4 {2}
 [0&1&2] 4 {1}
-State: 5
-[0&1&2] 4 {2}
-[0] 5 {2}
 --END--
 HOA: v1
 name: "FGa"
@ -741,7 +731,7 @@ State: 1
 --END--
 HOA: v1
 name: "(p0 W XXGp0) & G(Fp1 & FGp2)"
-States: 6
+States: 5
 Start: 0
 AP: 3 "p0" "p1" "p2"
 acc-name: parity max even 3
@ -750,23 +740,21 @@ properties: trans-labels explicit-labels trans-acc colored
 --BODY--
 State: 0
 [0] 0 {1}
-[t] 2 {1}
-[0&1&2] 3 {1}
+[!0] 1 {1}
+[0&1&2] 2 {1}
 State: 1
-[2] 4 {1}
-State: 2
+[t] 3 {1}
 [1&2] 4 {1}
-[t] 5 {1}
+State: 2
+[!0] 1 {1}
+[0&!1&2] 2 {1}
+[0&1&2] 2 {2}
 State: 3
-[2] 1 {1}
-[0&!1&2] 3 {1}
-[0&1&2] 3 {2}
+[0] 3 {1}
+[0&1&2] 4 {1}
 State: 4
 [0&!1&2] 4 {1}
 [0&1&2] 4 {2}
-State: 5
-[0&1&2] 4 {1}
-[0] 5 {1}
 --END--
 EOF
 diff expected2 res2
@ -1182,7 +1170,7 @@ State: 1
 --END--
 HOA: v1
 name: "(p0 W XXGp0) & G(Fp1 & FGp2)"
-States: 10
+States: 5
 Start: 0
 AP: 3 "p0" "p1" "p2"
 acc-name: Rabin 1
@ -1190,46 +1178,24 @@ Acceptance: 2 Fin(0) & Inf(1)
 properties: trans-labels explicit-labels trans-acc deterministic
 --BODY--
 State: 0
+[0&!1 | 0&!2] 0
 [!0] 1
-[0&!1 | 0&!2] 2
-[0&1&2] 3
+[0&1&2] 2
 State: 1
-[!1 | !2] 4
-[1&2] 5
+[!1 | !2] 3
+[1&2] 4
 State: 2
-[!0&!1 | !0&!2] 1
-[0&!1 | 0&!2] 2
-[0&1&2] 3
-[!0&1&2] 6
+[0&!2] 0 {0}
+[!0] 1
+[0&!1&2] 2
+[0&1&2] 2 {1}
 State: 3
-[!0&!2] 1
-[0&!2] 2 {0}
-[!0&!1&2] 7
-[!0&1&2] 8
-[0&!1&2] 9
-[0&1&2] 9 {1}
+[0&!1 | 0&!2] 3
+[0&1&2] 4
 State: 4
-[0&!1 | 0&!2] 4
-[0&1&2] 5
-State: 5
-[0&!2] 4 {0}
-[0&!1&2] 5
-[0&1&2] 5 {1}
-State: 6
-[!0&!1 | !2] 4
-[0&2 | 1&2] 5
-State: 7
-[!2] 4
-[2] 5
-State: 8
-[!2] 4
-[2] 5
-State: 9
-[!0&!2] 1
-[0&!2] 2 {0}
-[!0&2] 8
-[0&!1&2] 9
-[0&1&2] 9 {1}
+[0&!2] 3 {0}
+[0&!1&2] 4
+[0&1&2] 4 {1}
 --END--
 HOA: v1
 name: "FGa"
@ -1268,7 +1234,7 @@ State: 1
 --END--
 HOA: v1
 name: "(p0 W XXGp0) & G(Fp1 & FGp2)"
-States: 10
+States: 5
 Start: 0
 AP: 3 "p0" "p1" "p2"
 acc-name: Rabin 1
@ -1276,46 +1242,24 @@ Acceptance: 2 Fin(0) & Inf(1)
 properties: trans-labels explicit-labels trans-acc deterministic
 --BODY--
 State: 0
+[0&!1 | 0&!2] 0
 [!0] 1
-[0&!1 | 0&!2] 2
-[0&1&2] 3
+[0&1&2] 2
 State: 1
-[!1 | !2] 4
-[1&2] 5
+[!1 | !2] 3
+[1&2] 4
 State: 2
-[!0&!1 | !0&!2] 1
-[0&!1 | 0&!2] 2
-[0&1&2] 3
-[!0&1&2] 6
+[0&!2] 0 {0}
+[!0] 1
+[0&!1&2] 2
+[0&1&2] 2 {1}
 State: 3
-[!0&!2] 1
-[0&!2] 2 {0}
-[!0&!1&2] 7
-[!0&1&2] 8
-[0&!1&2] 9
-[0&1&2] 9 {1}
+[0&!1 | 0&!2] 3
+[0&1&2] 4
 State: 4
-[0&!1 | 0&!2] 4
-[0&1&2] 5
-State: 5
-[0&!2] 4 {0}
-[0&!1&2] 5
-[0&1&2] 5 {1}
-State: 6
-[!0&!1 | !2] 4
-[0&2 | 1&2] 5
-State: 7
-[!2] 4
-[2] 5
-State: 8
-[!2] 4
-[2] 5
-State: 9
-[!0&!2] 1
-[0&!2] 2 {0}
-[!0&2] 8
-[0&!1&2] 9
-[0&1&2] 9 {1}
+[0&!2] 3 {0}
+[0&!1&2] 4
+[0&1&2] 4 {1}
 --END--
 HOA: v1
 name: "FGa"
@ -1354,7 +1298,7 @@ State: 1
 --END--
 HOA: v1
 name: "(p0 W XXGp0) & G(Fp1 & FGp2)"
-States: 10
+States: 5
 Start: 0
 AP: 3 "p0" "p1" "p2"
 acc-name: parity max even 2
@ -1362,46 +1306,24 @@ Acceptance: 2 Fin(1) & Inf(0)
 properties: trans-labels explicit-labels trans-acc deterministic
 --BODY--
 State: 0
+[0&!1 | 0&!2] 0
 [!0] 1
-[0&!1 | 0&!2] 2
-[0&1&2] 3
+[0&1&2] 2
 State: 1
-[!1 | !2] 4
-[1&2] 5
+[!1 | !2] 3
+[1&2] 4
 State: 2
-[!0&!1 | !0&!2] 1
-[0&!1 | 0&!2] 2
-[0&1&2] 3
-[!0&1&2] 6
+[0&!2] 0 {1}
+[!0] 1
+[0&!1&2] 2
+[0&1&2] 2 {0}
 State: 3
-[!0&!2] 1
-[0&!2] 2 {1}
-[!0&!1&2] 7
-[!0&1&2] 8
-[0&!1&2] 9
-[0&1&2] 9 {0}
+[0&!1 | 0&!2] 3
+[0&1&2] 4
 State: 4
-[0&!1 | 0&!2] 4
-[0&1&2] 5
-State: 5
-[0&!2] 4 {1}
-[0&!1&2] 5
-[0&1&2] 5 {0}
-State: 6
-[!0&!1 | !2] 4
-[0&2 | 1&2] 5
-State: 7
-[!2] 4
-[2] 5
-State: 8
-[!2] 4
-[2] 5
-State: 9
-[!0&!2] 1
-[0&!2] 2 {1}
-[!0&2] 8
-[0&!1&2] 9
-[0&1&2] 9 {0}
+[0&!2] 3 {1}
+[0&!1&2] 4
+[0&1&2] 4 {0}
 --END--
 HOA: v1
 name: "FGa"
@ -1440,7 +1362,7 @@ State: 1
 --END--
 HOA: v1
 name: "(p0 W XXGp0) & G(Fp1 & FGp2)"
-States: 10
+States: 5
 Start: 0
 AP: 3 "p0" "p1" "p2"
 acc-name: parity min odd 3
@ -1449,46 +1371,24 @@ properties: trans-labels explicit-labels trans-acc colored
 properties: deterministic
 --BODY--
 State: 0
+[0&!1 | 0&!2] 0 {2}
 [!0] 1 {2}
-[0&!1 | 0&!2] 2 {2}
-[0&1&2] 3 {2}
+[0&1&2] 2 {2}
 State: 1
-[!1 | !2] 4 {2}
-[1&2] 5 {2}
+[!1 | !2] 3 {2}
+[1&2] 4 {2}
 State: 2
-[!0&!1 | !0&!2] 1 {2}
-[0&!1 | 0&!2] 2 {2}
-[0&1&2] 3 {2}
-[!0&1&2] 6 {2}
+[0&!2] 0 {0}
+[!0] 1 {2}
+[0&!1&2] 2 {2}
+[0&1&2] 2 {1}
 State: 3
-[!0&!2] 1 {2}
-[0&!2] 2 {0}
-[!0&!1&2] 7 {2}
-[!0&1&2] 8 {2}
-[0&!1&2] 9 {2}
-[0&1&2] 9 {1}
+[0&!1 | 0&!2] 3 {2}
+[0&1&2] 4 {2}
 State: 4
-[0&!1 | 0&!2] 4 {2}
-[0&1&2] 5 {2}
-State: 5
-[0&!2] 4 {0}
-[0&!1&2] 5 {2}
-[0&1&2] 5 {1}
-State: 6
-[!0&!1 | !2] 4 {2}
-[0&2 | 1&2] 5 {2}
-State: 7
-[!2] 4 {2}
-[2] 5 {2}
-State: 8
-[!2] 4 {2}
-[2] 5 {2}
-State: 9
-[!0&!2] 1 {2}
-[0&!2] 2 {0}
-[!0&2] 8 {2}
-[0&!1&2] 9 {2}
-[0&1&2] 9 {1}
+[0&!2] 3 {0}
+[0&!1&2] 4 {2}
+[0&1&2] 4 {1}
 --END--
 HOA: v1
 name: "FGa"
@ -1527,7 +1427,7 @@ State: 1
 --END--
 HOA: v1
 name: "(p0 W XXGp0) & G(Fp1 & FGp2)"
-States: 10
+States: 5
 Start: 0
 AP: 3 "p0" "p1" "p2"
 acc-name: parity min odd 3
@ -1536,46 +1436,24 @@ properties: trans-labels explicit-labels trans-acc colored
 properties: deterministic
 --BODY--
 State: 0
+[0&!1 | 0&!2] 0 {2}
 [!0] 1 {2}
-[0&!1 | 0&!2] 2 {2}
-[0&1&2] 3 {2}
+[0&1&2] 2 {2}
 State: 1
-[!1 | !2] 4 {2}
-[1&2] 5 {2}
+[!1 | !2] 3 {2}
+[1&2] 4 {2}
 State: 2
-[!0&!1 | !0&!2] 1 {2}
-[0&!1 | 0&!2] 2 {2}
-[0&1&2] 3 {2}
-[!0&1&2] 6 {2}
+[0&!2] 0 {0}
+[!0] 1 {2}
+[0&!1&2] 2 {2}
+[0&1&2] 2 {1}
 State: 3
-[!0&!2] 1 {2}
-[0&!2] 2 {0}
-[!0&!1&2] 7 {2}
-[!0&1&2] 8 {2}
-[0&!1&2] 9 {2}
-[0&1&2] 9 {1}
+[0&!1 | 0&!2] 3 {2}
+[0&1&2] 4 {2}
 State: 4
-[0&!1 | 0&!2] 4 {2}
-[0&1&2] 5 {2}
-State: 5
-[0&!2] 4 {0}
-[0&!1&2] 5 {2}
-[0&1&2] 5 {1}
-State: 6
-[!0&!1 | !2] 4 {2}
-[0&2 | 1&2] 5 {2}
-State: 7
-[!2] 4 {2}
-[2] 5 {2}
-State: 8
-[!2] 4 {2}
-[2] 5 {2}
-State: 9
-[!0&!2] 1 {2}
-[0&!2] 2 {0}
-[!0&2] 8 {2}
-[0&!1&2] 9 {2}
-[0&1&2] 9 {1}
+[0&!2] 3 {0}
+[0&!1&2] 4 {2}
+[0&1&2] 4 {1}
 --END--
 HOA: v1
 name: "FGa"
@ -1614,7 +1492,7 @@ State: 1
 --END--
 HOA: v1
 name: "(p0 W XXGp0) & G(Fp1 & FGp2)"
-States: 10
+States: 5
 Start: 0
 AP: 3 "p0" "p1" "p2"
 acc-name: parity max even 4
@ -1623,46 +1501,24 @@ properties: trans-labels explicit-labels trans-acc colored
 properties: deterministic
 --BODY--
 State: 0
+[0&!1 | 0&!2] 0 {1}
 [!0] 1 {1}
-[0&!1 | 0&!2] 2 {1}
-[0&1&2] 3 {1}
+[0&1&2] 2 {1}
 State: 1
-[!1 | !2] 4 {1}
-[1&2] 5 {1}
+[!1 | !2] 3 {1}
+[1&2] 4 {1}
 State: 2
-[!0&!1 | !0&!2] 1 {1}
-[0&!1 | 0&!2] 2 {1}
-[0&1&2] 3 {1}
-[!0&1&2] 6 {1}
+[0&!2] 0 {3}
+[!0] 1 {1}
+[0&!1&2] 2 {1}
+[0&1&2] 2 {2}
 State: 3
-[!0&!2] 1 {1}
-[0&!2] 2 {3}
-[!0&!1&2] 7 {1}
-[!0&1&2] 8 {1}
-[0&!1&2] 9 {1}
-[0&1&2] 9 {2}
+[0&!1 | 0&!2] 3 {1}
+[0&1&2] 4 {1}
 State: 4
-[0&!1 | 0&!2] 4 {1}
-[0&1&2] 5 {1}
-State: 5
-[0&!2] 4 {3}
-[0&!1&2] 5 {1}
-[0&1&2] 5 {2}
-State: 6
-[!0&!1 | !2] 4 {1}
-[0&2 | 1&2] 5 {1}
-State: 7
-[!2] 4 {1}
-[2] 5 {1}
-State: 8
-[!2] 4 {1}
-[2] 5 {1}
-State: 9
-[!0&!2] 1 {1}
-[0&!2] 2 {3}
-[!0&2] 8 {1}
-[0&!1&2] 9 {1}
-[0&1&2] 9 {2}
+[0&!2] 3 {3}
+[0&!1&2] 4 {1}
+[0&1&2] 4 {2}
 --END--
 EOF
 diff expected4 res4
--- a/tests/core/stutter-tgba.test
+++ b/tests/core/stutter-tgba.test
@ -26,13 +26,13 @@ ltl2tgba '!FG(a | Xa | G!a)' -H | autfilt -H --destut > pos.hoa
 ltl2tgba 'FG(a | Xa | G!a)' -H | autfilt -H --destut > neg.hoa
 autfilt pos.hoa --product neg.hoa -H > prod.hoa
 autfilt --is-empty prod.hoa -q && exit 1
-autfilt --states=7 prod.hoa -q
+autfilt --states=5 prod.hoa -q

 ltl2tgba '!FG(a | Xa | G!a)' -H | autfilt -H --instut > pos.hoa
 ltl2tgba 'FG(a | Xa | G!a)' -H | autfilt -H --instut > neg.hoa
 autfilt pos.hoa --product neg.hoa -H > prod.hoa
 autfilt --is-empty prod.hoa -q && exit 1
-autfilt --states=9 prod.hoa -q
+autfilt --states=6 prod.hoa -q


 # Check for issue #7.
--- a/tests/python/automata.ipynb
+++ b/tests/python/automata.ipynb
--- a/tests/python/highlighting.ipynb
+++ b/tests/python/highlighting.ipynb
--- a/tests/python/stutter-inv.ipynb
+++ b/tests/python/stutter-inv.ipynb
@ -302,7 +302,7 @@
       "</svg>\n"
      ],
      "text/plain": [
-       "<spot.impl.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7f31a00c1660> >"
+       "<spot.impl.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7f68605f5630> >"
      ]
     },
     "metadata": {},
@ -595,7 +595,7 @@
       "</svg>\n"
      ],
      "text/plain": [
-       "<spot.impl.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7f31a00c1b40> >"
+       "<spot.impl.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7f68605f5ae0> >"
      ]
     },
     "metadata": {},
@ -804,7 +804,7 @@
       "</svg>\n"
      ],
      "text/plain": [
-       "<spot.impl.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7f31a00c1b40> >"
+       "<spot.impl.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7f68605f5ae0> >"
      ]
     },
     "metadata": {},
@ -890,18 +890,18 @@
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       "<!-- Title: G(F(a &amp; Xa) &amp; F!a) Pages: 1 -->\n",
-       "<svg width=\"170pt\" height=\"178pt\"\n",
-       " viewBox=\"0.00 0.00 170.00 177.59\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
-       "<g id=\"graph0\" class=\"graph\" transform=\"scale(1 1) rotate(0) translate(4 173.5945)\">\n",
+       "<svg width=\"170pt\" height=\"145pt\"\n",
+       " viewBox=\"0.00 0.00 170.00 144.59\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
+       "<g id=\"graph0\" class=\"graph\" transform=\"scale(1 1) rotate(0) translate(4 140.5945)\">\n",
       "<title>G(F(a &amp; Xa) &amp; F!a)</title>\n",
-       "<polygon fill=\"#ffffff\" stroke=\"transparent\" points=\"-4,4 -4,-173.5945 166,-173.5945 166,4 -4,4\"/>\n",
-       "<text text-anchor=\"start\" x=\"25\" y=\"-155.3945\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">G(F(a &amp; Xa) &amp; F!a)</text>\n",
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-       "<text text-anchor=\"start\" x=\"72\" y=\"-141.3945\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">)&amp;Inf(</text>\n",
-       "<text text-anchor=\"start\" x=\"108\" y=\"-141.3945\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff4da0\">❶</text>\n",
-       "<text text-anchor=\"start\" x=\"124\" y=\"-141.3945\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">)</text>\n",
-       "<text text-anchor=\"start\" x=\"37\" y=\"-127.3945\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">[gen. Büchi 2]</text>\n",
+       "<polygon fill=\"#ffffff\" stroke=\"transparent\" points=\"-4,4 -4,-140.5945 166,-140.5945 166,4 -4,4\"/>\n",
+       "<text text-anchor=\"start\" x=\"25\" y=\"-122.3945\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">G(F(a &amp; Xa) &amp; F!a)</text>\n",
+       "<text text-anchor=\"start\" x=\"34\" y=\"-108.3945\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">Inf(</text>\n",
+       "<text text-anchor=\"start\" x=\"56\" y=\"-108.3945\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
+       "<text text-anchor=\"start\" x=\"72\" y=\"-108.3945\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">)&amp;Inf(</text>\n",
+       "<text text-anchor=\"start\" x=\"108\" y=\"-108.3945\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff4da0\">❶</text>\n",
+       "<text text-anchor=\"start\" x=\"124\" y=\"-108.3945\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">)</text>\n",
+       "<text text-anchor=\"start\" x=\"37\" y=\"-94.3945\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">[gen. Büchi 2]</text>\n",
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@ -918,17 +918,10 @@
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-       "<text text-anchor=\"start\" x=\"50.5\" y=\"-75.3945\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">!a</text>\n",
-       "<text text-anchor=\"start\" x=\"48\" y=\"-60.3945\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff4da0\">❶</text>\n",
-       "</g>\n",
-       "<!-- 0&#45;&gt;0 -->\n",
-       "<g id=\"edge3\" class=\"edge\">\n",
-       "<title>0&#45;&gt;0</title>\n",
-       "<path fill=\"none\" stroke=\"#000000\" d=\"M50.9906,-38.1717C47.5451,-59.3126 49.2148,-86.5945 56,-86.5945 62.043,-86.5945 64.0285,-64.9541 61.9564,-45.2852\"/>\n",
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-       "<text text-anchor=\"start\" x=\"52.5\" y=\"-90.3945\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">a</text>\n",
+       "<path fill=\"none\" stroke=\"#000000\" d=\"M49.6208,-37.6318C48.3189,-47.4524 50.4453,-56.5945 56,-56.5945 60.166,-56.5945 62.4036,-51.4521 62.7128,-44.7378\"/>\n",
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+       "<text text-anchor=\"start\" x=\"52.5\" y=\"-75.3945\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">a</text>\n",
+       "<text text-anchor=\"start\" x=\"48\" y=\"-60.3945\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
       "</g>\n",
       "<!-- 1 -->\n",
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@ -937,33 +930,33 @@
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       "</g>\n",
       "<!-- 0&#45;&gt;1 -->\n",
-       "<g id=\"edge4\" class=\"edge\">\n",
+       "<g id=\"edge3\" class=\"edge\">\n",
       "<title>0&#45;&gt;1</title>\n",
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-       "<text text-anchor=\"start\" x=\"92\" y=\"-24.3945\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
+       "<text text-anchor=\"start\" x=\"94.5\" y=\"-39.3945\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">!a</text>\n",
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       "<!-- 1&#45;&gt;0 -->\n",
-       "<g id=\"edge5\" class=\"edge\">\n",
+       "<g id=\"edge4\" class=\"edge\">\n",
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       "<!-- 1&#45;&gt;1 -->\n",
-       "<g id=\"edge6\" class=\"edge\">\n",
+       "<g id=\"edge5\" class=\"edge\">\n",
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-       "<text text-anchor=\"start\" x=\"136\" y=\"-60.3945\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
+       "<text text-anchor=\"start\" x=\"138.5\" y=\"-75.3945\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">!a</text>\n",
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       "</g>\n",
       "</svg>\n"
      ],
      "text/plain": [
-       "<spot.impl.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7f31a00c1630> >"
+       "<spot.impl.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7f68605f5a50> >"
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@ -1061,7 +1054,7 @@
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+       "<spot.impl.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7f68605f5b70> >"
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