translate, postproc: improve parity output

* spot/twaalgos/translate.cc: When producing Parity output, split LTL
as we do in the Generic case.
* spot/twaalgos/postproc.hh, spot/twaalgos/postproc.cc: Use
acd_transform() and add an "acd" option to disable this.
* bin/spot-x.cc, NEWS: Document this.
* tests/core/genltl.test, tests/core/minusx.test,
tests/core/parity2.test: Adjust test cases for improved outputs.

NEWS

@@ -164,11 +164,20 @@ New in spot 2.10.6.dev  (not yet released)
     further simplification.  This was introduced to help with automata
     produced from formulas output by "genltl --eil-gsi" (see above).
 
-  - spot::postproc has new configuration variable branch-post that
+  - spot::postprocessor has new configuration variable branch-post that
     can be used to control the use of branching-postponement (diabled
     by default) or delayed-branching (see above, enabled by default).
     See the spot-x(7) man page for details.
 
+  - spot::postprocessor is now using acd_transform() by default when
+    building parity automata.  Setting option "acd=0" will revert
+    to using "to_parity()" instead.
+
+  - When asked to build parity automata, spot::translator is now more
+    aggressively using LTL decomposition, as done in the Generic
+    acceptance case before paritizing the result.  This results in
+    much smaller automata in many cases.
+
   - spot::parallel_policy is an object that can be passed to some
     algorithm to specify how many threads can be used if Spot has been
     compiled with --enable-pthread.  Currently, only

bin/spot-x.cc

@@ -80,6 +80,9 @@ only if it is smaller than the original skeleton.  This option is only \
 used when comp-susp=1 and default to 1 or 2 depending on whether --small \
 or --deterministic is specified.") },
     { nullptr, 0, nullptr, 0, "Postprocessing options:", 0 },
+    { DOC("acd", "Set to 1 (the default) to use paritize automata using \
+the alternatinc cycle decomposition.  Set to 0 to use paritization based \
+on latest appearance record variants.") },
     { DOC("scc-filter", "Set to 1 (the default) to enable \
 SCC-pruning and acceptance simplification at the beginning of \
 post-processing.  Transitions that are outside of accepting SCC are \

spot/twaalgos/postproc.cc

@@ -1,5 +1,5 @@
 // -*- coding: utf-8 -*-
-// Copyright (C) 2012-2021 Laboratoire de Recherche et Développement
+// Copyright (C) 2012-2022 Laboratoire de Recherche et Développement
 // de l'Epita (LRDE).
 //
 // This file is part of Spot, a model checking library.
@@ -40,6 +40,7 @@
 #include <spot/twaalgos/cobuchi.hh>
 #include <spot/twaalgos/cleanacc.hh>
 #include <spot/twaalgos/toparity.hh>
+#include <spot/twaalgos/zlktree.hh>
 
 namespace spot
 {
@@ -92,6 +93,7 @@ namespace spot
         merge_states_min_ = opt->get("merge-states-min", 128);
         wdba_det_max_ = opt->get("wdba-det-max", 4096);
         simul_trans_pruning_ = opt->get("simul-trans-pruning", 512);
+        acd_ = opt->get("acd", 1);
 
         if (sat_acc_ && sat_minimize_ == 0)
           sat_minimize_ = 1;        // Dicho.
@@ -250,7 +252,8 @@ namespace spot
       tmp = ensure_ba(tmp);
     if (want_parity)
       {
-        reduce_parity_here(tmp, COLORED_);
+        if (!acd_was_used_)
+          reduce_parity_here(tmp, COLORED_);
         parity_kind kind = parity_kind_any;
         parity_style style = parity_style_any;
         if ((type_ & ParityMin) == ParityMin)
@@ -295,6 +298,8 @@ namespace spot
     bool via_gba =
       (type_ == Buchi) || (type_ == GeneralizedBuchi) || (type_ == Monitor);
     bool want_parity = type_ & Parity;
+    acd_was_used_ = false;
+
     if (COLORED_ && !want_parity)
       throw std::runtime_error("postprocessor: the Colored setting only works "
                                "for parity acceptance");
@@ -340,18 +345,26 @@ namespace spot
         !(type_ == Generic && PREF_ == Any && level_ == Low))
       a = remove_alternation(a);
 
+    // If we do want a parity automaton, we can use to_parity().
+    // However (1) degeneralization is faster if the input is
+    // GBA, and (2) if we want a deterministic parity automaton and the
+    // input is not deterministic, that is useless here.  We need
+    // to determinize it first, and our deterministization
+    // function only deal with TGBA as input.
     if ((via_gba || (want_parity && !a->acc().is_parity()))
         && !a->acc().is_generalized_buchi())
       {
-        // If we do want a parity automaton, we can use to_parity().
-        // However (1) degeneralization is better if the input is
-        // GBA, and (2) if we want a deterministic parity automaton and the
-        // input is not deterministic, that is useless here.  We need
-        // to determinize it first, and our deterministization
-        // function only deal with TGBA as input.
         if (want_parity && (PREF_ != Deterministic || is_deterministic(a)))
           {
-            a = to_parity(a);
+            if (acd_)
+              {
+                a = acd_transform(a, COLORED_);
+                acd_was_used_ = true;
+              }
+            else
+              {
+                a = to_parity(a);
+              }
           }
         else
           {

spot/twaalgos/postproc.hh

@@ -270,6 +270,8 @@ namespace spot
     int simul_max_ = 4096;
     int merge_states_min_ = 128;
     int wdba_det_max_ = 4096;
+    bool acd_ = false;
+    bool acd_was_used_;
   };
   /// @}
 }

spot/twaalgos/translate.cc

@@ -137,6 +137,9 @@ namespace spot
     twa_graph_ptr aut;
     twa_graph_ptr aut2 = nullptr;
 
+    bool split_hard =
+      type_ == Generic || (type_ & Parity) || type_ == GeneralizedBuchi;
+
     if (ltl_split_ && !r.is_syntactic_obligation())
       {
         formula r2 = r;
@@ -146,11 +149,11 @@ namespace spot
             r2 = r2[0];
             ++leading_x;
           }
-        if (type_ == Generic || type_ == GeneralizedBuchi)
+        if (split_hard)
           {
-            // F(q|u|f) = q|F(u)|F(f)  only for generic acceptance
+            // F(q|u|f) = q|F(u)|F(f)  disabled for GeneralizedBuchi
             // G(q&e&f) = q&G(e)&G(f)
-            bool want_u = r2.is({op::F, op::Or}) && (type_ == Generic);
+            bool want_u = r2.is({op::F, op::Or}) && (type_ != GeneralizedBuchi);
             if (want_u || r2.is({op::G, op::And}))
               {
                 std::vector<formula> susp;
@@ -213,20 +216,19 @@ namespace spot
             oblg.erase(i, oblg.end());
           }
 
+        // The only cases where we accept susp and rest to be both
+        // non-empty is when doing Generic/Parity/TGBA
         if (!susp.empty())
           {
-            // The only cases where we accept susp and rest to be both
+            if (!rest.empty() && !split_hard)
-            // non-empty is when doing Generic acceptance or TGBA.
-            if (!rest.empty()
-                && !(type_ == Generic || type_ == GeneralizedBuchi))
               {
                 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)
+            //if (rest.empty() && type_ & Parity)
-              susp = { formula::multop(r2.kind(), susp) };
+            //  susp = { formula::multop(r2.kind(), susp) };
           }
         // For TGBA and BA, we only split if there is something to
         // suspend.

tests/core/genltl.test

@@ -190,29 +190,29 @@ cat >exp<<EOF
 "ms-example=4,2",10,10
 "ms-example=4,3",11,11
 "ms-example=4,4",12,12
-"ms-phi-r=0",1,2
+"ms-phi-r=0",1,1
-"ms-phi-r=1",1,12
+"ms-phi-r=1",1,2
-"ms-phi-r=2",1,28
+"ms-phi-r=2",1,5
-"ms-phi-s=0",1,3
+"ms-phi-s=0",1,1
-"ms-phi-s=1",1,7
+"ms-phi-s=1",1,2
-"ms-phi-s=2",1,484
+"ms-phi-s=2",1,5
 "ms-phi-h=0",1,1
 "ms-phi-h=1",2,3
 "ms-phi-h=2",4,7
 "ms-phi-h=3",8,15
 "ms-phi-h=4",16,31
 "gf-equiv=0",1,1
-"gf-equiv=1",1,3
+"gf-equiv=1",1,2
-"gf-equiv=2",1,7
+"gf-equiv=2",1,5
-"gf-equiv=3",1,20
+"gf-equiv=3",1,10
-"gf-equiv=4",1,80
+"gf-equiv=4",1,17
-"gf-equiv=5",1,430
+"gf-equiv=5",1,26
 "gf-implies=0",1,1
-"gf-implies=1",1,4
+"gf-implies=1",1,1
-"gf-implies=2",1,11
+"gf-implies=2",1,2
-"gf-implies=3",1,33
+"gf-implies=3",1,3
-"gf-implies=4",1,131
+"gf-implies=4",1,4
-"gf-implies=5",1,653
+"gf-implies=5",1,5
 "gf-equiv-xn=1",2,2
 "gf-equiv-xn=2",4,4
 "gf-equiv-xn=3",8,8

tests/core/minusx.test

@@ -1,7 +1,7 @@
 #!/bin/sh
 # -*- coding: utf-8 -*-
-# Copyright (C) 2016, 2020, 2021 Laboratoire de Recherche et Développement de
+# Copyright (C) 2016, 2020-2022 Laboratoire de Recherche et
-# l'Epita (LRDE).
+# Développement de l'Epita (LRDE).
 #
 # This file is part of Spot, a model checking library.
 #
@@ -41,9 +41,9 @@ test 4,1 = `ltl2tgba --stats=%s,%d "$f"`
 test 6,0 = `ltl2tgba -x wdba-det-max=4 --stats=%s,%d "$f"`
 
 # Make sure simul-max has an effect
-f=`genltl --ms-phi-s=2`
+f=`genltl --ms-phi-h=8`
-test 484 -eq `ltl2tgba -P -D --stats=%s "$f"`
+test 511 -eq `ltl2tgba -P -D --stats=%s "$f"`
-test 484 -lt `ltl2tgba -P -D -x simul-max=512 --stats=%s "$f"`
+test 511 -lt `ltl2tgba -P -D -x simul-max=512 --stats=%s "$f"`
 
 # Illustrate issue #455: the simulation-based reduction applied before
 # tba-det can cause the creation of a DBA that is harder to reduce.

tests/core/parity2.test

@@ -1,6 +1,6 @@
 #!/bin/sh
 # -*- coding: utf-8 -*-
-# Copyright (C) 2018-2019, 2021 Laboratoire de Recherche et
+# Copyright (C) 2018-2019, 2021, 2022 Laboratoire de Recherche et
 # Développement de l'Epita (LRDE).
 #
 # This file is part of Spot, a model checking library.
@@ -65,30 +65,24 @@ State: 1
 --END--
 HOA: v1
 name: "(p0 W XXGp0) & G(Fp1 & FGp2)"
-States: 5
+States: 3
 Start: 0
 AP: 3 "p0" "p1" "p2"
-acc-name: Buchi
+acc-name: Rabin 1
-Acceptance: 1 Inf(0)
+Acceptance: 2 Fin(0) & Inf(1)
-properties: trans-labels explicit-labels trans-acc
+properties: trans-labels explicit-labels trans-acc deterministic
 --BODY--
 State: 0
-[0] 0
+[0&!1&2] 0
+[0&!2] 0 {0}
+[0&1&2] 0 {1}
 [!0] 1
-[0&1&2] 2
 State: 1
-[t] 3
+[t] 2
-[1&2] 4
 State: 2
-[!0] 1
 [0&!1&2] 2
-[0&1&2] 2 {0}
+[0&!2] 2 {0}
-State: 3
+[0&1&2] 2 {1}
-[0] 3
-[0&1&2] 4
-State: 4
-[0&!1&2] 4
-[0&1&2] 4 {0}
 --END--
 HOA: v1
 name: "FGa"
@@ -124,30 +118,24 @@ State: 1
 --END--
 HOA: v1
 name: "(p0 W XXGp0) & G(Fp1 & FGp2)"
-States: 5
+States: 3
 Start: 0
 AP: 3 "p0" "p1" "p2"
 acc-name: Rabin 1
 Acceptance: 2 Fin(0) & Inf(1)
-properties: trans-labels explicit-labels trans-acc
+properties: trans-labels explicit-labels trans-acc deterministic
 --BODY--
 State: 0
-[0] 0
+[0&!1&2] 0
+[0&!2] 0 {0}
+[0&1&2] 0 {1}
 [!0] 1
-[0&1&2] 2
 State: 1
-[t] 3
+[t] 2
-[1&2] 4
 State: 2
-[!0] 1
 [0&!1&2] 2
+[0&!2] 2 {0}
 [0&1&2] 2 {1}
-State: 3
-[0] 3
-[0&1&2] 4
-State: 4
-[0&!1&2] 4
-[0&1&2] 4 {1}
 --END--
 HOA: v1
 name: "FGa"
@@ -183,30 +171,24 @@ State: 1
 --END--
 HOA: v1
 name: "(p0 W XXGp0) & G(Fp1 & FGp2)"
-States: 5
+States: 3
 Start: 0
 AP: 3 "p0" "p1" "p2"
-acc-name: Buchi
+acc-name: parity max even 2
-Acceptance: 1 Inf(0)
+Acceptance: 2 Fin(1) & Inf(0)
-properties: trans-labels explicit-labels trans-acc
+properties: trans-labels explicit-labels trans-acc deterministic
 --BODY--
 State: 0
-[0] 0
+[0&!1&2] 0
+[0&1&2] 0 {0}
+[0&!2] 0 {1}
 [!0] 1
-[0&1&2] 2
 State: 1
-[t] 3
+[t] 2
-[1&2] 4
 State: 2
-[!0] 1
 [0&!1&2] 2
 [0&1&2] 2 {0}
-State: 3
+[0&!2] 2 {1}
-[0] 3
-[0&1&2] 4
-State: 4
-[0&!1&2] 4
-[0&1&2] 4 {0}
 --END--
 HOA: v1
 name: "FGa"
@@ -242,30 +224,25 @@ State: 1
 --END--
 HOA: v1
 name: "(p0 W XXGp0) & G(Fp1 & FGp2)"
-States: 5
+States: 3
 Start: 0
 AP: 3 "p0" "p1" "p2"
-acc-name: Streett 1
+acc-name: parity min odd 3
-Acceptance: 2 Fin(0) | Inf(1)
+Acceptance: 3 Fin(0) & (Inf(1) | Fin(2))
 properties: trans-labels explicit-labels trans-acc colored
+properties: deterministic
 --BODY--
 State: 0
-[0] 0 {0}
+[0&!1&2] 0 {2}
-[!0] 1 {0}
+[0&!2] 0 {0}
-[0&1&2] 2 {0}
+[0&1&2] 0 {1}
+[!0] 1 {2}
 State: 1
-[t] 3 {0}
+[t] 2 {2}
-[1&2] 4 {0}
 State: 2
-[!0] 1 {0}
+[0&!1&2] 2 {2}
-[0&!1&2] 2 {0}
+[0&!2] 2 {0}
 [0&1&2] 2 {1}
-State: 3
-[0] 3 {0}
-[0&1&2] 4 {0}
-State: 4
-[0&!1&2] 4 {0}
-[0&1&2] 4 {1}
 --END--
 HOA: v1
 name: "FGa"
@@ -301,30 +278,25 @@ State: 1
 --END--
 HOA: v1
 name: "(p0 W XXGp0) & G(Fp1 & FGp2)"
-States: 5
+States: 3
 Start: 0
 AP: 3 "p0" "p1" "p2"
 acc-name: parity min odd 3
 Acceptance: 3 Fin(0) & (Inf(1) | Fin(2))
 properties: trans-labels explicit-labels trans-acc colored
+properties: deterministic
 --BODY--
 State: 0
-[0] 0 {2}
+[0&!1&2] 0 {2}
+[0&!2] 0 {0}
+[0&1&2] 0 {1}
 [!0] 1 {2}
-[0&1&2] 2 {2}
 State: 1
-[t] 3 {2}
+[t] 2 {2}
-[1&2] 4 {2}
 State: 2
-[!0] 1 {2}
 [0&!1&2] 2 {2}
+[0&!2] 2 {0}
 [0&1&2] 2 {1}
-State: 3
-[0] 3 {2}
-[0&1&2] 4 {2}
-State: 4
-[0&!1&2] 4 {2}
-[0&1&2] 4 {1}
 --END--
 HOA: v1
 name: "FGa"
@@ -360,30 +332,25 @@ State: 1
 --END--
 HOA: v1
 name: "(p0 W XXGp0) & G(Fp1 & FGp2)"
-States: 5
+States: 3
 Start: 0
 AP: 3 "p0" "p1" "p2"
-acc-name: parity max even 3
+acc-name: parity max even 4
-Acceptance: 3 Inf(2) | (Fin(1) & Inf(0))
+Acceptance: 4 Fin(3) & (Inf(2) | (Fin(1) & Inf(0)))
 properties: trans-labels explicit-labels trans-acc colored
+properties: deterministic
 --BODY--
 State: 0
-[0] 0 {1}
+[0&!1&2] 0 {1}
+[0&1&2] 0 {2}
+[0&!2] 0 {3}
 [!0] 1 {1}
-[0&1&2] 2 {1}
 State: 1
-[t] 3 {1}
+[t] 2 {1}
-[1&2] 4 {1}
 State: 2
-[!0] 1 {1}
 [0&!1&2] 2 {1}
 [0&1&2] 2 {2}
-State: 3
+[0&!2] 2 {3}
-[0] 3 {1}
-[0&1&2] 4 {1}
-State: 4
-[0&!1&2] 4 {1}
-[0&1&2] 4 {2}
 --END--
 EOF
 
@@ -777,7 +744,7 @@ State: 0
 HOA: v1
 name: "G(Fa & Fb)"
 States: 2
-Start: 1
+Start: 0
 AP: 2 "a" "b"
 acc-name: Buchi
 Acceptance: 1 Inf(0)
@@ -786,15 +753,15 @@ properties: deterministic stutter-invariant
 --BODY--
 State: 0
 [!1] 0
-[1] 1 {0}
+[0&1] 0 {0}
+[!0&1] 1
 State: 1
-[0&!1] 0
+[0] 0 {0}
 [!0] 1
-[0&1] 1 {0}
 --END--
 HOA: v1
 name: "(p0 W XXGp0) & G(Fp1 & FGp2)"
-States: 5
+States: 3
 Start: 0
 AP: 3 "p0" "p1" "p2"
 acc-name: Rabin 1
@@ -802,24 +769,16 @@ Acceptance: 2 Fin(0) & Inf(1)
 properties: trans-labels explicit-labels trans-acc deterministic
 --BODY--
 State: 0
-[0&!1 | 0&!2] 0
+[0&!1&2] 0
-[!0] 1
-[0&1&2] 2
-State: 1
-[!1 | !2] 3
-[1&2] 4
-State: 2
 [0&!2] 0 {0}
+[0&1&2] 0 {1}
 [!0] 1
+State: 1
+[t] 2
+State: 2
 [0&!1&2] 2
+[0&!2] 2 {0}
 [0&1&2] 2 {1}
-State: 3
-[0&!1 | 0&!2] 3
-[0&1&2] 4
-State: 4
-[0&!2] 3 {0}
-[0&!1&2] 4
-[0&1&2] 4 {1}
 --END--
 HOA: v1
 name: "FGa"
@@ -838,7 +797,7 @@ State: 0
 HOA: v1
 name: "G(Fa & Fb)"
 States: 2
-Start: 1
+Start: 0
 AP: 2 "a" "b"
 acc-name: Rabin 1
 Acceptance: 2 Fin(0) & Inf(1)
@@ -847,15 +806,15 @@ properties: deterministic stutter-invariant
 --BODY--
 State: 0
 [!1] 0
-[1] 1 {1}
+[0&1] 0 {1}
+[!0&1] 1
 State: 1
-[0&!1] 0
+[0] 0 {1}
 [!0] 1
-[0&1] 1 {1}
 --END--
 HOA: v1
 name: "(p0 W XXGp0) & G(Fp1 & FGp2)"
-States: 5
+States: 3
 Start: 0
 AP: 3 "p0" "p1" "p2"
 acc-name: Rabin 1
@@ -863,24 +822,16 @@ Acceptance: 2 Fin(0) & Inf(1)
 properties: trans-labels explicit-labels trans-acc deterministic
 --BODY--
 State: 0
-[0&!1 | 0&!2] 0
+[0&!1&2] 0
-[!0] 1
-[0&1&2] 2
-State: 1
-[!1 | !2] 3
-[1&2] 4
-State: 2
 [0&!2] 0 {0}
+[0&1&2] 0 {1}
 [!0] 1
+State: 1
+[t] 2
+State: 2
 [0&!1&2] 2
+[0&!2] 2 {0}
 [0&1&2] 2 {1}
-State: 3
-[0&!1 | 0&!2] 3
-[0&1&2] 4
-State: 4
-[0&!2] 3 {0}
-[0&!1&2] 4
-[0&1&2] 4 {1}
 --END--
 HOA: v1
 name: "FGa"
@@ -899,7 +850,7 @@ State: 0
 HOA: v1
 name: "G(Fa & Fb)"
 States: 2
-Start: 1
+Start: 0
 AP: 2 "a" "b"
 acc-name: Buchi
 Acceptance: 1 Inf(0)
@@ -908,15 +859,15 @@ properties: deterministic stutter-invariant
 --BODY--
 State: 0
 [!1] 0
-[1] 1 {0}
+[0&1] 0 {0}
+[!0&1] 1
 State: 1
-[0&!1] 0
+[0] 0 {0}
 [!0] 1
-[0&1] 1 {0}
 --END--
 HOA: v1
 name: "(p0 W XXGp0) & G(Fp1 & FGp2)"
-States: 5
+States: 3
 Start: 0
 AP: 3 "p0" "p1" "p2"
 acc-name: parity max even 2
@@ -924,24 +875,16 @@ Acceptance: 2 Fin(1) & Inf(0)
 properties: trans-labels explicit-labels trans-acc deterministic
 --BODY--
 State: 0
-[0&!1 | 0&!2] 0
+[0&!1&2] 0
-[!0] 1
+[0&1&2] 0 {0}
-[0&1&2] 2
-State: 1
-[!1 | !2] 3
-[1&2] 4
-State: 2
 [0&!2] 0 {1}
 [!0] 1
+State: 1
+[t] 2
+State: 2
 [0&!1&2] 2
 [0&1&2] 2 {0}
-State: 3
+[0&!2] 2 {1}
-[0&!1 | 0&!2] 3
-[0&1&2] 4
-State: 4
-[0&!2] 3 {1}
-[0&!1&2] 4
-[0&1&2] 4 {0}
 --END--
 HOA: v1
 name: "FGa"
@@ -960,7 +903,7 @@ State: 0
 HOA: v1
 name: "G(Fa & Fb)"
 States: 2
-Start: 1
+Start: 0
 AP: 2 "a" "b"
 acc-name: Streett 1
 Acceptance: 2 Fin(0) | Inf(1)
@@ -969,15 +912,15 @@ properties: deterministic stutter-invariant
 --BODY--
 State: 0
 [!1] 0 {0}
-[1] 1 {1}
+[0&1] 0 {1}
+[!0&1] 1 {0}
 State: 1
-[0&!1] 0 {0}
+[0] 0 {1}
 [!0] 1 {0}
-[0&1] 1 {1}
 --END--
 HOA: v1
 name: "(p0 W XXGp0) & G(Fp1 & FGp2)"
-States: 5
+States: 3
 Start: 0
 AP: 3 "p0" "p1" "p2"
 acc-name: parity min odd 3
@@ -986,24 +929,16 @@ properties: trans-labels explicit-labels trans-acc colored
 properties: deterministic
 --BODY--
 State: 0
-[0&!1 | 0&!2] 0 {2}
+[0&!1&2] 0 {2}
-[!0] 1 {2}
-[0&1&2] 2 {2}
-State: 1
-[!1 | !2] 3 {2}
-[1&2] 4 {2}
-State: 2
 [0&!2] 0 {0}
+[0&1&2] 0 {1}
 [!0] 1 {2}
+State: 1
+[t] 2 {2}
+State: 2
 [0&!1&2] 2 {2}
+[0&!2] 2 {0}
 [0&1&2] 2 {1}
-State: 3
-[0&!1 | 0&!2] 3 {2}
-[0&1&2] 4 {2}
-State: 4
-[0&!2] 3 {0}
-[0&!1&2] 4 {2}
-[0&1&2] 4 {1}
 --END--
 HOA: v1
 name: "FGa"
@@ -1022,7 +957,7 @@ State: 0
 HOA: v1
 name: "G(Fa & Fb)"
 States: 2
-Start: 1
+Start: 0
 AP: 2 "a" "b"
 acc-name: parity min odd 3
 Acceptance: 3 Fin(0) & (Inf(1) | Fin(2))
@@ -1031,15 +966,15 @@ properties: deterministic stutter-invariant
 --BODY--
 State: 0
 [!1] 0 {2}
-[1] 1 {1}
+[0&1] 0 {1}
+[!0&1] 1 {2}
 State: 1
-[0&!1] 0 {2}
+[0] 0 {1}
 [!0] 1 {2}
-[0&1] 1 {1}
 --END--
 HOA: v1
 name: "(p0 W XXGp0) & G(Fp1 & FGp2)"
-States: 5
+States: 3
 Start: 0
 AP: 3 "p0" "p1" "p2"
 acc-name: parity min odd 3
@@ -1048,24 +983,16 @@ properties: trans-labels explicit-labels trans-acc colored
 properties: deterministic
 --BODY--
 State: 0
-[0&!1 | 0&!2] 0 {2}
+[0&!1&2] 0 {2}
-[!0] 1 {2}
-[0&1&2] 2 {2}
-State: 1
-[!1 | !2] 3 {2}
-[1&2] 4 {2}
-State: 2
 [0&!2] 0 {0}
+[0&1&2] 0 {1}
 [!0] 1 {2}
+State: 1
+[t] 2 {2}
+State: 2
 [0&!1&2] 2 {2}
+[0&!2] 2 {0}
 [0&1&2] 2 {1}
-State: 3
-[0&!1 | 0&!2] 3 {2}
-[0&1&2] 4 {2}
-State: 4
-[0&!2] 3 {0}
-[0&!1&2] 4 {2}
-[0&1&2] 4 {1}
 --END--
 HOA: v1
 name: "FGa"
@@ -1084,7 +1011,7 @@ State: 0
 HOA: v1
 name: "G(Fa & Fb)"
 States: 2
-Start: 1
+Start: 0
 AP: 2 "a" "b"
 acc-name: parity max even 3
 Acceptance: 3 Inf(2) | (Fin(1) & Inf(0))
@@ -1093,15 +1020,15 @@ properties: deterministic stutter-invariant
 --BODY--
 State: 0
 [!1] 0 {1}
-[1] 1 {2}
+[0&1] 0 {2}
+[!0&1] 1 {1}
 State: 1
-[0&!1] 0 {1}
+[0] 0 {2}
 [!0] 1 {1}
-[0&1] 1 {2}
 --END--
 HOA: v1
 name: "(p0 W XXGp0) & G(Fp1 & FGp2)"
-States: 5
+States: 3
 Start: 0
 AP: 3 "p0" "p1" "p2"
 acc-name: parity max even 4
@@ -1110,24 +1037,16 @@ properties: trans-labels explicit-labels trans-acc colored
 properties: deterministic
 --BODY--
 State: 0
-[0&!1 | 0&!2] 0 {1}
+[0&!1&2] 0 {1}
-[!0] 1 {1}
+[0&1&2] 0 {2}
-[0&1&2] 2 {1}
-State: 1
-[!1 | !2] 3 {1}
-[1&2] 4 {1}
-State: 2
 [0&!2] 0 {3}
 [!0] 1 {1}
+State: 1
+[t] 2 {1}
+State: 2
 [0&!1&2] 2 {1}
 [0&1&2] 2 {2}
-State: 3
+[0&!2] 2 {3}
-[0&!1 | 0&!2] 3 {1}
-[0&1&2] 4 {1}
-State: 4
-[0&!2] 3 {3}
-[0&!1&2] 4 {1}
-[0&1&2] 4 {2}
 --END--
 EOF
 diff expected3 res3