From a325de8678eac5946e06567ae4cd3a13eced60f0 Mon Sep 17 00:00:00 2001
From: Alexandre Duret-Lutz <adl@lrde.epita.fr>
Date: Fri, 22 Jun 2018 17:09:18 +0200
Subject: [PATCH] postproc: simplify the acceptance condition

* spot/twaalgos/postproc.cc: Here.
* spot/twaalgos/cobuchi.cc, spot/twaalgos/totgba.cc: Fix some bug
uncovered by the new simplified automata.
* tests/core/satmin2.test, tests/core/sccdot.test,
tests/core/sim3.test, tests/python/decompose.ipynb,
tests/python/satmin.ipynb: Update expected results.
* NEWS: Mention the simplification and the bug.
---
 NEWS                         |    9 +-
 spot/twaalgos/cobuchi.cc     |   10 +-
 spot/twaalgos/postproc.cc    |   23 +
 spot/twaalgos/totgba.cc      |   47 +-
 tests/core/satmin2.test      |    3 +-
 tests/core/sccdot.test       |    2 +-
 tests/core/sim3.test         |   14 +-
 tests/python/decompose.ipynb |  236 ++--
 tests/python/satmin.ipynb    | 2583 ++++++++++++++++------------------
 9 files changed, 1397 insertions(+), 1530 deletions(-)

diff --git a/NEWS b/NEWS
index 86a57d9e0..4276cd9c9 100644
--- a/NEWS
+++ b/NEWS
@@ -116,6 +116,10 @@ New in spot 2.5.3.dev  (not yet released)
     FG(a|b)|FG(!a|Xb)|FG(a|XXb)               21       4         4
     FG(a|b)|FG(!a|Xb)|FG(a|XXb)|FG(!a|XXXb)  170       8         8
 
+  - The automaton postprocessor will now simplify acceptance
+    conditions more aggressively, calling spot::simplify_acceptance()
+    or spot::cleanup_acceptance() depanding on the optimization level.
+
   - print_dot(), used to print automata in GraphViz's format,
     underwent several changes:
 
@@ -216,7 +220,10 @@ New in spot 2.5.3.dev  (not yet released)
   - The HOA parser will now accept Alias: declarations that occur
     before AP:.
 
-  - the option --allow-dups of randltl now works properly
+  - The option --allow-dups of randltl now works properly.
+
+  - Converting generalized-co-Büchi to Streett using dnf_to_nca()
+    could produce bogus automata if the input had rejecting SCCs.
 
   Deprecation notice:
 
diff --git a/spot/twaalgos/cobuchi.cc b/spot/twaalgos/cobuchi.cc
index 40b0d86a7..9fab6b64d 100644
--- a/spot/twaalgos/cobuchi.cc
+++ b/spot/twaalgos/cobuchi.cc
@@ -133,7 +133,7 @@ namespace spot
         product_states* res_map_;               // States of the aug. sub. cons.
         scc_info si_;                           // SCC information.
         unsigned nb_states_;                    // Number of states.
-        unsigned was_rabin_;                    // Was it Rabin before Streett?
+        unsigned was_dnf_;                      // Was it DNF before Streett?
         std::vector<unsigned>* orig_states_;    // Match old Rabin st. from new.
         std::vector<unsigned>* orig_clauses_;   // Associated Rabin clauses.
         unsigned orig_num_st_;                  // Rabin original nb states.
@@ -148,7 +148,7 @@ namespace spot
             bv->set(state);
           unsigned clause = 0;
           unsigned state = st.first;
-          if (was_rabin_)
+          if (was_dnf_)
             {
               clause = (*orig_clauses_)[state];
               assert((int)clause >= 0);
@@ -194,7 +194,7 @@ namespace spot
                              const const_twa_graph_ptr ref_power,
                              std::vector<acc_cond::rs_pair>& pairs,
                              bool named_states = false,
-                             bool was_rabin = false,
+                             bool was_dnf = false,
                              unsigned orig_num_st = 0)
           : aut_(ref_prod),
             state_based_(aut_->prop_state_acc().is_true()),
@@ -206,10 +206,10 @@ namespace spot
             si_(res_, (scc_info_options::TRACK_STATES
                        | scc_info_options::TRACK_SUCCS)),
             nb_states_(res_->num_states()),
-            was_rabin_(was_rabin),
+            was_dnf_(was_dnf),
             orig_num_st_(orig_num_st ? orig_num_st : ref_prod->num_states())
         {
-          if (was_rabin)
+          if (was_dnf)
             {
               orig_states_ = ref_prod->get_named_prop<std::vector<unsigned>>
                 ("original-states");
diff --git a/spot/twaalgos/postproc.cc b/spot/twaalgos/postproc.cc
index 9ed38dbee..0c14af47f 100644
--- a/spot/twaalgos/postproc.cc
+++ b/spot/twaalgos/postproc.cc
@@ -39,6 +39,7 @@
 #include <spot/twaalgos/parity.hh>
 #include <spot/twaalgos/cobuchi.hh>
 #include <spot/twaalgos/rabin2parity.hh>
+#include <spot/twaalgos/cleanacc.hh>
 
 namespace spot
 {
@@ -230,6 +231,27 @@ namespace spot
       throw std::runtime_error("postprocessor: the Colored setting only works "
                                "for parity acceptance");
 
+
+
+    // Attempt to simplify the acceptance condition, unless this is a
+    // parity automaton and we want parity acceptance in the output.
+    auto simplify_acc = [&](twa_graph_ptr in)
+      {
+        if (PREF_ == Any && level_ == Low)
+          return in;
+        if (!(want_parity && in->acc().is_parity()))
+          {
+            if (level_ == High)
+              return simplify_acceptance(in);
+            else
+              return cleanup_acceptance(in);
+          }
+        if (level_ == High)
+          return cleanup_parity(in);
+        return in;
+      };
+    a = simplify_acc(a);
+
     if (!a->is_existential() &&
         // We will probably have to revisit this condition later.
         // Currently, the intent is that postprocessor should never
@@ -438,6 +460,7 @@ namespace spot
       {
         dba = tgba_determinize(to_generalized_buchi(sim),
                                false, det_scc_, det_simul_, det_stutter_);
+        dba = simplify_acc(dba);
         if (level_ != Low)
           dba = simulation(dba);
         sim = nullptr;
diff --git a/spot/twaalgos/totgba.cc b/spot/twaalgos/totgba.cc
index 1b4022cbf..4e2c6c802 100644
--- a/spot/twaalgos/totgba.cc
+++ b/spot/twaalgos/totgba.cc
@@ -76,35 +76,32 @@ namespace spot
       void
       split_dnf_clauses(const acc_cond::acc_code& code)
       {
-        bool one_conjunction = false;
-        const acc_cond::acc_op root_op = code.back().sub.op;
-        auto s = code.back().sub.size;
-        while (s)
+        auto pos = &code.back();
+        if (pos->sub.op == acc_cond::acc_op::Or)
+          --pos;
+        auto start = &code.front();
+        while (pos > start)
           {
-            --s;
-            if (code[s].sub.op == acc_cond::acc_op::And
-                || ((one_conjunction = root_op == acc_cond::acc_op::And)))
+            const unsigned short size = pos[0].sub.size;
+            if (pos[0].sub.op == acc_cond::acc_op::And)
               {
-                s = one_conjunction ? s + 1 : s;
-                const unsigned short size = code[s].sub.size;
                 acc_cond::mark_t fin = {};
                 acc_cond::mark_t inf = {};
-                for (unsigned i = 1; i <= size; i += 2)
+                for (int i = 1; i <= (int)size; i += 2)
                   {
-                    if (code[s-i].sub.op == acc_cond::acc_op::Fin)
-                      fin |= code[s-i-1].mark;
-                    else if (code[s-i].sub.op == acc_cond::acc_op::Inf)
-                      inf |= code[s-i-1].mark;
+                    if (pos[-i].sub.op == acc_cond::acc_op::Fin)
+                      fin |= pos[-i - 1].mark;
+                    else if (pos[-i].sub.op == acc_cond::acc_op::Inf)
+                      inf |= pos[-i - 1].mark;
                     else
                       SPOT_UNREACHABLE();
                   }
                 all_clauses_.emplace_back(fin, inf);
                 set_to_keep_.emplace_back(fin | inf);
-                s -= size;
               }
-            else if (code[s].sub.op == acc_cond::acc_op::Fin) // Fin
+            else if (pos[0].sub.op == acc_cond::acc_op::Fin) // Fin
               {
-                auto m1 = code[--s].mark;
+                auto m1 = pos[-1].mark;
                 for (unsigned int s : m1.sets())
                   {
                     all_clauses_.emplace_back(acc_cond::mark_t({s}),
@@ -112,9 +109,9 @@ namespace spot
                     set_to_keep_.emplace_back(acc_cond::mark_t({s}));
                   }
               }
-            else if (code[s].sub.op == acc_cond::acc_op::Inf) // Inf
+            else if (pos[0].sub.op == acc_cond::acc_op::Inf) // Inf
               {
-                auto m2 = code[--s].mark;
+                auto m2 = pos[-1].mark;
                 all_clauses_.emplace_back(acc_cond::mark_t({}), m2);
                 set_to_keep_.emplace_back(m2);
               }
@@ -122,6 +119,7 @@ namespace spot
               {
                 SPOT_UNREACHABLE();
               }
+            pos -= size + 1;
           }
 #if TRACE
         trace << "\nPrinting all clauses\n";
@@ -244,10 +242,12 @@ namespace spot
         trace << "accepting clauses\n";
         for (unsigned i = 0; i < res.size(); ++i)
           {
-            trace << "scc(" << i << ") --> ";
+            trace << "scc(" << i << ") -->";
             for (auto elt : res[i])
-              trace << elt << ',';
-            trace << '\n'
+              trace << ' ' << elt;
+            if (si_.is_rejecting_scc(i))
+              trace << " rej";
+            trace << '\n';
           }
         trace << '\n';
 #endif
@@ -341,6 +341,7 @@ namespace spot
           {
             if (!si_.is_useful_scc(scc))
               continue;
+            trace << "scc #" << scc << '\n';
 
             bool rej_scc = acc_clauses_[scc].empty();
             for (auto st : si_.states_of(scc))
@@ -388,7 +389,7 @@ namespace spot
 
                         acc_cond::mark_t m = {};
                         if (same_scc || state_based_)
-                          m = all_set_to_add_;
+                          m = e.acc | all_set_to_add_;
 
                         for (const auto& p_dst : st_repr_[e.dst])
                           res_->new_edge(src, p_dst.second, e.cond, m);
diff --git a/tests/core/satmin2.test b/tests/core/satmin2.test
index 42f9958e9..113e23d86 100755
--- a/tests/core/satmin2.test
+++ b/tests/core/satmin2.test
@@ -335,7 +335,8 @@ HOA: v1
 States: 1
 Start: 0
 AP: 1 "a"
-Acceptance: 2 (Inf(0) & Fin(1)) | (Fin(0) & Inf(1))
+acc-name: generalized-co-Buchi 2
+Acceptance: 2 Fin(0)|Fin(1)
 properties: trans-labels explicit-labels trans-acc colored complete
 properties: deterministic
 --BODY--
diff --git a/tests/core/sccdot.test b/tests/core/sccdot.test
index 073a4820b..03fb2318a 100755
--- a/tests/core/sccdot.test
+++ b/tests/core/sccdot.test
@@ -156,7 +156,7 @@ HOA: v1
 States: 8
 Start: 0
 AP: 2 "a" "b"
-Acceptance: 3 (Inf(0)&Inf(1)) & Fin(2)
+Acceptance: 3 Fin(2) & (Inf(0)&Inf(1))
 properties: trans-labels explicit-labels trans-acc
 --BODY--
 State: 0
diff --git a/tests/core/sim3.test b/tests/core/sim3.test
index 147863a8a..c692e017c 100755
--- a/tests/core/sim3.test
+++ b/tests/core/sim3.test
@@ -1,7 +1,7 @@
 #! /bin/sh
 # -*- coding: utf-8 -*-
-# Copyright (C) 2015 Laboratoire de Recherche et Développement de
-# l'Epita (LRDE).
+# Copyright (C) 2015, 2018 Laboratoire de Recherche et Développement
+# de l'Epita (LRDE).
 #
 # This file is part of Spot, a model checking library.
 #
@@ -55,25 +55,25 @@ HOA: v1
 States: 5
 Start: 0
 AP: 2 "b" "a"
-acc-name: Rabin 2
-Acceptance: 4 (Fin(0) & Inf(1)) | (Fin(2) & Inf(3))
+acc-name: Streett 1
+Acceptance: 2 Fin(0) | Inf(1)
 properties: trans-labels explicit-labels state-acc complete
 properties: deterministic
 --BODY--
 State: 0
 [!1] 1
 [1] 3
-State: 1 {1 3}
+State: 1 {1}
 [0&!1] 1
 [!0&!1] 2
 [0&1] 3
 [!0&1] 4
-State: 2 {1}
+State: 2
 [0&!1] 1
 [!0&!1] 2
 [0&1] 3
 [!0&1] 4
-State: 3 {0 3}
+State: 3 {0 1}
 [0&!1] 1
 [!0&!1] 2
 [0&1] 3
diff --git a/tests/python/decompose.ipynb b/tests/python/decompose.ipynb
index 5b562d771..577ea6a67 100644
--- a/tests/python/decompose.ipynb
+++ b/tests/python/decompose.ipynb
@@ -200,7 +200,7 @@
        "</svg>\n"
       ],
       "text/plain": [
-       "<spot.impl.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7f6b42fa8f00> >"
+       "<spot.impl.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7fd3d85c40f0> >"
       ]
      },
      "execution_count": 2,
@@ -330,7 +330,7 @@
        "</svg>\n"
       ],
       "text/plain": [
-       "<spot.impl.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7f6b42f5f4b0> >"
+       "<spot.impl.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7fd3d85c40c0> >"
       ]
      },
      "execution_count": 3,
@@ -489,7 +489,7 @@
        "</svg>\n"
       ],
       "text/plain": [
-       "<spot.impl.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7f6b42f5f720> >"
+       "<spot.impl.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7fd3d860a060> >"
       ]
      },
      "execution_count": 4,
@@ -587,7 +587,7 @@
        "</svg>\n"
       ],
       "text/plain": [
-       "<spot.impl.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7f6b42f5fae0> >"
+       "<spot.impl.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7fd3d85c4120> >"
       ]
      },
      "execution_count": 5,
@@ -669,7 +669,7 @@
        "</svg>\n"
       ],
       "text/plain": [
-       "<spot.impl.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7f6b42f50bd0> >"
+       "<spot.impl.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7fd3d8571690> >"
       ]
      },
      "execution_count": 6,
@@ -796,7 +796,7 @@
        "</svg>\n"
       ],
       "text/plain": [
-       "<spot.impl.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7f6b437fb030> >"
+       "<spot.impl.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7fd3d8571360> >"
       ]
      },
      "metadata": {},
@@ -941,7 +941,7 @@
        "</svg>\n"
       ],
       "text/plain": [
-       "<spot.impl.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7f6b42fb30c0> >"
+       "<spot.impl.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7fd3d860a240> >"
       ]
      },
      "metadata": {},
@@ -1109,7 +1109,7 @@
        "</svg>\n"
       ],
       "text/plain": [
-       "<spot.impl.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7f6b437fb030> >"
+       "<spot.impl.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7fd3d862fed0> >"
       ]
      },
      "metadata": {},
@@ -1512,7 +1512,7 @@
        "</svg>\n"
       ],
       "text/plain": [
-       "<spot.impl.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7f6b42f7a780> >"
+       "<spot.impl.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7fd3d8571540> >"
       ]
      },
      "execution_count": 8,
@@ -1942,7 +1942,7 @@
        "</svg>\n"
       ],
       "text/plain": [
-       "<spot.impl.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7f6b42f7a8a0> >"
+       "<spot.impl.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7fd3d85c4030> >"
       ]
      },
      "metadata": {},
@@ -2174,7 +2174,7 @@
        "</svg>\n"
       ],
       "text/plain": [
-       "<spot.impl.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7f6b437fb030> >"
+       "<spot.impl.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7fd3d85c4150> >"
       ]
      },
      "metadata": {},
@@ -2384,7 +2384,7 @@
        "</svg>\n"
       ],
       "text/plain": [
-       "<spot.impl.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7f6b42f5f5a0> >"
+       "<spot.impl.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7fd3d85bbfc0> >"
       ]
      },
      "metadata": {},
@@ -2772,7 +2772,7 @@
        "</svg>\n"
       ],
       "text/plain": [
-       "<spot.impl.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7f6b42f0a5a0> >"
+       "<spot.impl.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7fd3d8571a80> >"
       ]
      },
      "execution_count": 10,
@@ -2788,7 +2788,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "The weak automata seem to be good candidates for further simplification.  Let's add a call to `postprocess()` to out decomposition loop, trying to preserve the determinism and state-based acceptance of the original automaton."
+    "The weak automata seem to be good candidates for further simplification.  Let's add a call to `postprocess()` to our decomposition loop, trying to preserve the determinism and state-based acceptance of the original automaton."
    ]
   },
   {
@@ -2933,7 +2933,7 @@
        "</svg>\n"
       ],
       "text/plain": [
-       "<spot.impl.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7f6b42fb30c0> >"
+       "<spot.impl.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7fd3d8571bd0> >"
       ]
      },
      "metadata": {},
@@ -3072,7 +3072,7 @@
        "</svg>\n"
       ],
       "text/plain": [
-       "<spot.impl.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7f6b42fa8f30> >"
+       "<spot.impl.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7fd3d8571b10> >"
       ]
      },
      "metadata": {},
@@ -3093,16 +3093,14 @@
        "<title>strong</title>\n",
        "<polygon fill=\"#ffffff\" stroke=\"transparent\" points=\"-4,4 -4,-332 901.6224,-332 901.6224,4 -4,4\"/>\n",
        "<text text-anchor=\"start\" x=\"428.3112\" y=\"-313.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">strong</text>\n",
-       "<text text-anchor=\"start\" x=\"332.3112\" y=\"-299.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">(Fin(</text>\n",
-       "<text text-anchor=\"start\" x=\"360.3112\" y=\"-299.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
-       "<text text-anchor=\"start\" x=\"376.3112\" y=\"-299.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">) &amp; Inf(</text>\n",
-       "<text text-anchor=\"start\" x=\"419.3112\" y=\"-299.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff4da0\">❶</text>\n",
-       "<text text-anchor=\"start\" x=\"435.3112\" y=\"-299.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">)) | (Fin(</text>\n",
-       "<text text-anchor=\"start\" x=\"482.3112\" y=\"-299.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff7f00\">❷</text>\n",
-       "<text text-anchor=\"start\" x=\"498.3112\" y=\"-299.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">) &amp; Inf(</text>\n",
-       "<text text-anchor=\"start\" x=\"541.3112\" y=\"-299.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#6a3d9a\">❸</text>\n",
-       "<text text-anchor=\"start\" x=\"557.3112\" y=\"-299.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">))</text>\n",
-       "<text text-anchor=\"start\" x=\"419.8112\" y=\"-285.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">[Rabin 2]</text>\n",
+       "<text text-anchor=\"start\" x=\"366.8112\" y=\"-299.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">Inf(</text>\n",
+       "<text text-anchor=\"start\" x=\"388.8112\" y=\"-299.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
+       "<text text-anchor=\"start\" x=\"404.8112\" y=\"-299.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">) | (Fin(</text>\n",
+       "<text text-anchor=\"start\" x=\"447.8112\" y=\"-299.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff4da0\">❶</text>\n",
+       "<text text-anchor=\"start\" x=\"463.8112\" y=\"-299.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">) &amp; Inf(</text>\n",
+       "<text text-anchor=\"start\" x=\"506.8112\" y=\"-299.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff7f00\">❷</text>\n",
+       "<text text-anchor=\"start\" x=\"522.8112\" y=\"-299.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">))</text>\n",
+       "<text text-anchor=\"start\" x=\"388.8112\" y=\"-285.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">[parity min even 3]</text>\n",
        "<g id=\"clust1\" class=\"cluster\">\n",
        "<title>cluster_0</title>\n",
        "<polygon fill=\"none\" stroke=\"#00ff00\" points=\"284,-38 284,-243 889.6224,-243 889.6224,-38 284,-38\"/>\n",
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@@ -3282,7 +3280,7 @@
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@@ -4018,7 +4016,7 @@
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@@ -5664,12 +5662,12 @@
     "# `decompose_scc()` by SCC number\n",
     "\n",
     "Decompose SCC can also be called by SCC numbers.\n",
-    "The example below show the different SCC numbers and the state they contains, before extracting the sub-automaton containing SCC 1 and 2 (i.e., anything leading to states 1 and 4 of the original automaton).  This example also shows that when an `scc_info` is available for to automaton to decompose, it can be passed to `decompose_scc()` in lieu of the automaton: doing so is faster because `decompose_scc()` does not need to rebuild this object. "
+    "The example below show the different SCC numbers and the state they contains, before extracting the sub-automaton containing SCC 0 and 2 (i.e., anything leading to states 1 and 4 of the original automaton).  This example also shows that when an `scc_info` is available for to automaton to decompose, it can be passed to `decompose_scc()` in lieu of the automaton: doing so is faster because `decompose_scc()` does not need to rebuild this object. "
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   {
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-   "execution_count": 21,
+   "execution_count": 22,
    "metadata": {},
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        "</g>\n",
        "<!-- I&#45;&gt;0 -->\n",
        "<g id=\"edge1\" class=\"edge\">\n",
        "<title>I&#45;&gt;0</title>\n",
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        "</g>\n",
        "<!-- 0&#45;&gt;0 -->\n",
        "<g id=\"edge2\" class=\"edge\">\n",
        "<title>0&#45;&gt;0</title>\n",
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-       "<text text-anchor=\"start\" x=\"36\" y=\"-181.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">!a &amp; !c</text>\n",
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        "</g>\n",
        "<!-- 1 -->\n",
        "<g id=\"node3\" class=\"node\">\n",
        "<title>1</title>\n",
-       "<ellipse fill=\"#ffffaa\" stroke=\"#000000\" cx=\"192\" cy=\"-34\" rx=\"18\" ry=\"18\"/>\n",
-       "<text text-anchor=\"middle\" x=\"192\" y=\"-30.3\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">1</text>\n",
+       "<ellipse fill=\"#ffffaa\" stroke=\"#000000\" cx=\"393\" cy=\"-46\" rx=\"18\" ry=\"18\"/>\n",
+       "<text text-anchor=\"middle\" x=\"393\" y=\"-42.3\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">1</text>\n",
        "</g>\n",
        "<!-- 0&#45;&gt;1 -->\n",
        "<g id=\"edge3\" class=\"edge\">\n",
        "<title>0&#45;&gt;1</title>\n",
-       "<path fill=\"none\" stroke=\"#000000\" d=\"M70.2973,-130.6462C94.7464,-111.2308 144.6248,-71.6215 172.3348,-49.6165\"/>\n",
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-       "<text text-anchor=\"start\" x=\"92\" y=\"-117.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">a &amp; b &amp; !c</text>\n",
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+       "<text text-anchor=\"start\" x=\"202.5\" y=\"-3.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">c</text>\n",
        "</g>\n",
        "<!-- 2 -->\n",
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        "<title>2</title>\n",
-       "<ellipse fill=\"#ffffaa\" stroke=\"#000000\" cx=\"267\" cy=\"-149\" rx=\"18\" ry=\"18\"/>\n",
-       "<text text-anchor=\"middle\" x=\"267\" y=\"-145.3\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">2</text>\n",
+       "<ellipse fill=\"#ffffaa\" stroke=\"#000000\" cx=\"206\" cy=\"-56\" rx=\"18\" ry=\"18\"/>\n",
+       "<text text-anchor=\"middle\" x=\"206\" y=\"-52.3\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">2</text>\n",
        "</g>\n",
        "<!-- 0&#45;&gt;2 -->\n",
        "<g id=\"edge4\" class=\"edge\">\n",
        "<title>0&#45;&gt;2</title>\n",
-       "<path fill=\"none\" stroke=\"#000000\" d=\"M74.3558,-142.609C112.1732,-143.8636 198.8193,-146.7381 241.8285,-148.1649\"/>\n",
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-       "<text text-anchor=\"start\" x=\"174\" y=\"-150.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">a &amp; !c</text>\n",
+       "<path fill=\"none\" stroke=\"#000000\" d=\"M74.0935,-47.2062C100.6718,-48.9781 150.3801,-52.292 180.604,-54.3069\"/>\n",
+       "<polygon fill=\"#000000\" stroke=\"#000000\" points=\"187.8423,-54.7895 180.6483,-57.4668 184.3501,-54.5566 180.8578,-54.3238 180.8578,-54.3238 180.8578,-54.3238 184.3501,-54.5566 181.0674,-51.1807 187.8423,-54.7895 187.8423,-54.7895\"/>\n",
+       "<text text-anchor=\"start\" x=\"113\" y=\"-55.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">a &amp; !c</text>\n",
        "</g>\n",
        "<!-- 1&#45;&gt;1 -->\n",
        "<g id=\"edge5\" class=\"edge\">\n",
        "<title>1&#45;&gt;1</title>\n",
-       "<path fill=\"none\" stroke=\"#000000\" d=\"M185.2664,-51.0373C183.8922,-60.8579 186.1367,-70 192,-70 196.3975,-70 198.7594,-64.8576 199.0858,-58.1433\"/>\n",
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-       "<text text-anchor=\"start\" x=\"187.5\" y=\"-88.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">b</text>\n",
-       "<text text-anchor=\"start\" x=\"184\" y=\"-73.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
+       "<path fill=\"none\" stroke=\"#000000\" d=\"M385.9688,-62.6641C384.4063,-72.625 386.75,-82 393,-82 397.6875,-82 400.1777,-76.7266 400.4707,-69.8876\"/>\n",
+       "<polygon fill=\"#000000\" stroke=\"#000000\" points=\"400.0313,-62.6641 403.6006,-69.4598 400.2438,-66.1576 400.4564,-69.6511 400.4564,-69.6511 400.4564,-69.6511 400.2438,-66.1576 397.3122,-69.8425 400.0313,-62.6641 400.0313,-62.6641\"/>\n",
+       "<text text-anchor=\"start\" x=\"388.5\" y=\"-100.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">1</text>\n",
+       "<text text-anchor=\"start\" x=\"385\" y=\"-85.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
        "</g>\n",
        "<!-- 3 -->\n",
        "<g id=\"node4\" class=\"node\">\n",
        "<title>3</title>\n",
-       "<ellipse fill=\"#ffffaa\" stroke=\"#000000\" cx=\"371\" cy=\"-149\" rx=\"18\" ry=\"18\"/>\n",
-       "<text text-anchor=\"middle\" x=\"371\" y=\"-145.3\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">3</text>\n",
+       "<ellipse fill=\"#ffffaa\" stroke=\"#000000\" cx=\"310\" cy=\"-46\" rx=\"18\" ry=\"18\"/>\n",
+       "<text text-anchor=\"middle\" x=\"310\" y=\"-42.3\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">3</text>\n",
+       "</g>\n",
+       "<!-- 3&#45;&gt;1 -->\n",
+       "<g id=\"edge10\" class=\"edge\">\n",
+       "<title>3&#45;&gt;1</title>\n",
+       "<path fill=\"none\" stroke=\"#000000\" d=\"M328.0098,-46C339.5679,-46 354.7507,-46 367.5345,-46\"/>\n",
+       "<polygon fill=\"#000000\" stroke=\"#000000\" points=\"374.7388,-46 367.7388,-49.1501 371.2388,-46 367.7388,-46.0001 367.7388,-46.0001 367.7388,-46.0001 371.2388,-46 367.7387,-42.8501 374.7388,-46 374.7388,-46\"/>\n",
+       "<text text-anchor=\"start\" x=\"346\" y=\"-49.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">!a</text>\n",
        "</g>\n",
        "<!-- 3&#45;&gt;3 -->\n",
-       "<g id=\"edge9\" class=\"edge\">\n",
+       "<g id=\"edge11\" class=\"edge\">\n",
        "<title>3&#45;&gt;3</title>\n",
-       "<path fill=\"none\" stroke=\"#000000\" d=\"M362.0212,-164.916C359.679,-175.1504 362.6719,-185 371,-185 377.3762,-185 380.625,-179.2263 380.7465,-171.9268\"/>\n",
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-       "<text text-anchor=\"start\" x=\"367.5\" y=\"-188.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">a</text>\n",
+       "<path fill=\"none\" stroke=\"#000000\" d=\"M302.9688,-62.6641C301.4063,-72.625 303.75,-82 310,-82 314.6875,-82 317.1777,-76.7266 317.4707,-69.8876\"/>\n",
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+       "<text text-anchor=\"start\" x=\"306.5\" y=\"-85.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">a</text>\n",
        "</g>\n",
        "<!-- 2&#45;&gt;0 -->\n",
        "<g id=\"edge6\" class=\"edge\">\n",
        "<title>2&#45;&gt;0</title>\n",
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-       "<text text-anchor=\"start\" x=\"172\" y=\"-171.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">!a &amp; !c</text>\n",
+       "<path fill=\"none\" stroke=\"#000000\" d=\"M189.0754,-62.434C169.992,-68.8187 138.0894,-76.8678 111,-71 99.6726,-68.5464 87.8767,-63.5531 78.1272,-58.6697\"/>\n",
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+       "<text text-anchor=\"start\" x=\"111\" y=\"-76.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">!a &amp; !c</text>\n",
+       "</g>\n",
+       "<!-- 2&#45;&gt;1 -->\n",
+       "<g id=\"edge7\" class=\"edge\">\n",
+       "<title>2&#45;&gt;1</title>\n",
+       "<path fill=\"none\" stroke=\"#000000\" d=\"M219.0266,-68.4976C242.5652,-89.4912 293.6722,-127.7847 336,-109 354.8745,-100.6237 370.1522,-82.5674 380.1221,-67.9237\"/>\n",
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+       "<text text-anchor=\"start\" x=\"292\" y=\"-117.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">!a &amp; c</text>\n",
        "</g>\n",
        "<!-- 2&#45;&gt;3 -->\n",
-       "<g id=\"edge8\" class=\"edge\">\n",
+       "<g id=\"edge9\" class=\"edge\">\n",
        "<title>2&#45;&gt;3</title>\n",
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-       "<text text-anchor=\"start\" x=\"303\" y=\"-152.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">a &amp; c</text>\n",
+       "<path fill=\"none\" stroke=\"#000000\" d=\"M224.1154,-54.2581C240.8642,-52.6477 265.92,-50.2385 284.6521,-48.4373\"/>\n",
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+       "<text text-anchor=\"start\" x=\"242\" y=\"-55.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">a &amp; c</text>\n",
        "</g>\n",
        "<!-- 2&#45;&gt;2 -->\n",
-       "<g id=\"edge7\" class=\"edge\">\n",
+       "<g id=\"edge8\" class=\"edge\">\n",
        "<title>2&#45;&gt;2</title>\n",
-       "<path fill=\"none\" stroke=\"#000000\" d=\"M260.6208,-166.0373C259.3189,-175.8579 261.4453,-185 267,-185 271.166,-185 273.4036,-179.8576 273.7128,-173.1433\"/>\n",
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-       "<text text-anchor=\"start\" x=\"249\" y=\"-188.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">a &amp; !c</text>\n",
+       "<path fill=\"none\" stroke=\"#000000\" d=\"M199.6208,-73.0373C198.3189,-82.8579 200.4453,-92 206,-92 210.166,-92 212.4036,-86.8576 212.7128,-80.1433\"/>\n",
+       "<polygon fill=\"#000000\" stroke=\"#000000\" points=\"212.3792,-73.0373 215.8541,-79.8818 212.5434,-76.5335 212.7076,-80.0296 212.7076,-80.0296 212.7076,-80.0296 212.5434,-76.5335 209.561,-80.1774 212.3792,-73.0373 212.3792,-73.0373\"/>\n",
+       "<text text-anchor=\"start\" x=\"188\" y=\"-95.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">a &amp; !c</text>\n",
        "</g>\n",
        "</g>\n",
        "</svg>\n"
       ],
       "text/plain": [
-       "<spot.impl.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7f6b42f6c900> >"
+       "<spot.impl.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7fd3d860a240> >"
       ]
      },
-     "execution_count": 21,
+     "execution_count": 22,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -5985,7 +5997,7 @@
     "for scc in range(si.scc_count()):\n",
     "    print(\"SCC #{} containts states {}\".format(scc, list(si.states_of(scc))))\n",
     "display(aut)\n",
-    "spot.decompose_scc(si, '1,2')"
+    "spot.decompose_scc(si, '0,2')"
    ]
   },
   {
@@ -5997,7 +6009,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 22,
+   "execution_count": 23,
    "metadata": {},
    "outputs": [
     {
@@ -6074,10 +6086,10 @@
        "</svg>\n"
       ],
       "text/plain": [
-       "<spot.impl.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7f6b42f2c150> >"
+       "<spot.impl.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7fd3d850d8d0> >"
       ]
      },
-     "execution_count": 22,
+     "execution_count": 23,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -6103,7 +6115,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.6.5"
+   "version": "3.6.5+"
   }
  },
  "nbformat": 4,
diff --git a/tests/python/satmin.ipynb b/tests/python/satmin.ipynb
index a34f9d170..16e9e44a5 100644
--- a/tests/python/satmin.ipynb
+++ b/tests/python/satmin.ipynb
@@ -256,7 +256,7 @@
        "</svg>\n"
       ],
       "text/plain": [
-       "<spot.impl.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7f7b085aaea0> >"
+       "<spot.impl.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7f79c85a5150> >"
       ]
      },
      "execution_count": 3,
@@ -444,7 +444,7 @@
        "</svg>\n"
       ],
       "text/plain": [
-       "<spot.impl.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7f7b0861fc90> >"
+       "<spot.impl.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7f79c857fb40> >"
       ]
      },
      "execution_count": 4,
@@ -680,7 +680,7 @@
        "</svg>\n"
       ],
       "text/plain": [
-       "<spot.impl.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7f7b085b5060> >"
+       "<spot.impl.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7f79c85d20f0> >"
       ]
      },
      "execution_count": 5,
@@ -913,7 +913,7 @@
        "</svg>\n"
       ],
       "text/plain": [
-       "<spot.impl.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7f7b08561b70> >"
+       "<spot.impl.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7f79c857f5d0> >"
       ]
      },
      "execution_count": 6,
@@ -973,96 +973,95 @@
        "<!-- 0 -->\n",
        "<g id=\"node2\" class=\"node\">\n",
        "<title>0</title>\n",
-       "<ellipse fill=\"#ffffaa\" stroke=\"#000000\" cx=\"74.25\" cy=\"-32.0026\" rx=\"18\" ry=\"18\"/>\n",
-       "<text text-anchor=\"middle\" x=\"74.25\" y=\"-28.3026\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">0</text>\n",
+       "<ellipse fill=\"#ffffaa\" stroke=\"#000000\" cx=\"88.75\" cy=\"-32.0026\" rx=\"18\" ry=\"18\"/>\n",
+       "<text text-anchor=\"middle\" x=\"88.75\" y=\"-28.3026\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">0</text>\n",
        "</g>\n",
        "<!-- I&#45;&gt;0 -->\n",
        "<g id=\"edge1\" class=\"edge\">\n",
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       "text/plain": [
-       "<spot.impl.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7f7b08561bd0> >"
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      "execution_count": 9,
@@ -1470,9 +1462,9 @@
        "      <td>NaN</td>\n",
        "      <td>NaN</td>\n",
        "      <td>NaN</td>\n",
-       "      <td>1428</td>\n",
-       "      <td>73430</td>\n",
-       "      <td>4</td>\n",
+       "      <td>996</td>\n",
+       "      <td>48806</td>\n",
+       "      <td>2</td>\n",
        "      <td>0</td>\n",
        "      <td>1</td>\n",
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@@ -1484,11 +1476,11 @@
        "      <td>5</td>\n",
        "      <td>16</td>\n",
        "      <td>40</td>\n",
-       "      <td>3960</td>\n",
-       "      <td>336307</td>\n",
-       "      <td>13</td>\n",
-       "      <td>1</td>\n",
-       "      <td>19</td>\n",
+       "      <td>2760</td>\n",
+       "      <td>224707</td>\n",
+       "      <td>9</td>\n",
+       "      <td>0</td>\n",
+       "      <td>6</td>\n",
        "      <td>0</td>\n",
        "    </tr>\n",
        "    <tr>\n",
@@ -1496,13 +1488,13 @@
        "      <td>5</td>\n",
        "      <td>4</td>\n",
        "      <td>4</td>\n",
-       "      <td>12</td>\n",
+       "      <td>11</td>\n",
        "      <td>32</td>\n",
        "      <td>2008</td>\n",
-       "      <td>116372</td>\n",
-       "      <td>5</td>\n",
+       "      <td>155020</td>\n",
+       "      <td>6</td>\n",
        "      <td>0</td>\n",
-       "      <td>4</td>\n",
+       "      <td>7</td>\n",
        "      <td>0</td>\n",
        "    </tr>\n",
        "  </tbody>\n",
@@ -1511,14 +1503,14 @@
       ],
       "text/plain": [
        "  input.states target.states reachable.states edges transitions variables  \\\n",
-       "0            6             3              NaN   NaN         NaN      1428   \n",
-       "1            6             5                5    16          40      3960   \n",
-       "2            5             4                4    12          32      2008   \n",
+       "0            6             3              NaN   NaN         NaN       996   \n",
+       "1            6             5                5    16          40      2760   \n",
+       "2            5             4                4    11          32      2008   \n",
        "\n",
        "  clauses enc.user enc.sys sat.user sat.sys  \n",
-       "0   73430        4       0        1       0  \n",
-       "1  336307       13       1       19       0  \n",
-       "2  116372        5       0        4       0  "
+       "0   48806        2       0        1       0  \n",
+       "1  224707        9       0        6       0  \n",
+       "2  155020        6       0        7       0  "
       ]
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-       "<spot.impl.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7f7b0cb8d6f0> >"
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       "text/plain": [
-       "<spot.impl.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7f7b0cb8dc00> >"
+       "<spot.impl.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7f79cdb107b0> >"
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      "execution_count": 11,
@@ -1994,13 +1949,13 @@
        "      <td>2</td>\n",
        "      <td>5</td>\n",
        "      <td>5</td>\n",
-       "      <td>18</td>\n",
+       "      <td>16</td>\n",
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-       "      <td>3050</td>\n",
-       "      <td>437037</td>\n",
-       "      <td>20</td>\n",
+       "      <td>2300</td>\n",
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-       "      <td>17</td>\n",
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        "      <td>0</td>\n",
        "    </tr>\n",
        "    <tr>\n",
@@ -2010,9 +1965,9 @@
        "      <td>2</td>\n",
        "      <td>6</td>\n",
        "      <td>16</td>\n",
-       "      <td>488</td>\n",
-       "      <td>28449</td>\n",
-       "      <td>2</td>\n",
+       "      <td>368</td>\n",
+       "      <td>17993</td>\n",
+       "      <td>1</td>\n",
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@@ -2024,8 +1979,8 @@
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-       "      <td>68</td>\n",
-       "      <td>1285</td>\n",
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@@ -2037,14 +1992,14 @@
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        "  input.states target.states reachable.states edges transitions variables  \\\n",
-       "0            2             5                5    18          40      3050   \n",
-       "1            2             2                2     6          16       488   \n",
-       "2            2             1              NaN   NaN         NaN        68   \n",
+       "0            2             5                5    16          40      2300   \n",
+       "1            2             2                2     6          16       368   \n",
+       "2            2             1              NaN   NaN         NaN        92   \n",
        "\n",
        "  clauses enc.user enc.sys sat.user sat.sys  \n",
-       "0  437037       20       0       17       0  \n",
-       "1   28449        2       0        0       0  \n",
-       "2    1285        0       0        0       0  "
+       "0  285287       13       0        9       0  \n",
+       "1   17993        1       0        0       0  \n",
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@@ -2205,54 +2160,40 @@
        "      <th>0</th>\n",
        "      <td>6</td>\n",
        "      <td>6</td>\n",
+       "      <td>5</td>\n",
+       "      <td>13</td>\n",
+       "      <td>40</td>\n",
+       "      <td>2742</td>\n",
+       "      <td>173183</td>\n",
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-       "      <td>19</td>\n",
-       "      <td>48</td>\n",
-       "      <td>3894</td>\n",
-       "      <td>258719</td>\n",
-       "      <td>9</td>\n",
        "      <td>0</td>\n",
-       "      <td>6</td>\n",
+       "      <td>3</td>\n",
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        "    </tr>\n",
        "    <tr>\n",
        "      <th>1</th>\n",
-       "      <td>6</td>\n",
-       "      <td>5</td>\n",
-       "      <td>5</td>\n",
-       "      <td>15</td>\n",
-       "      <td>40</td>\n",
-       "      <td>2005</td>\n",
-       "      <td>106302</td>\n",
-       "      <td>5</td>\n",
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-       "      <td>2</td>\n",
-       "      <td>0</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>2</th>\n",
        "      <td>5</td>\n",
        "      <td>4</td>\n",
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        "      <td>32</td>\n",
-       "      <td>676</td>\n",
-       "      <td>24632</td>\n",
-       "      <td>1</td>\n",
+       "      <td>964</td>\n",
+       "      <td>45412</td>\n",
+       "      <td>2</td>\n",
+       "      <td>0</td>\n",
        "      <td>0</td>\n",
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        "      <td>0</td>\n",
        "    </tr>\n",
        "    <tr>\n",
-       "      <th>3</th>\n",
+       "      <th>2</th>\n",
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        "      <td>NaN</td>\n",
        "      <td>363</td>\n",
-       "      <td>10553</td>\n",
-       "      <td>0</td>\n",
+       "      <td>10496</td>\n",
+       "      <td>1</td>\n",
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        "      <td>0</td>\n",
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@@ -2263,16 +2204,14 @@
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-       "0            6             6                6    19          48      3894   \n",
-       "1            6             5                5    15          40      2005   \n",
-       "2            5             4                4    11          32       676   \n",
-       "3            4             3              NaN   NaN         NaN       363   \n",
+       "0            6             6                5    13          40      2742   \n",
+       "1            5             4                4    11          32       964   \n",
+       "2            4             3              NaN   NaN         NaN       363   \n",
        "\n",
        "  clauses enc.user enc.sys sat.user sat.sys  \n",
-       "0  258719        9       0        6       0  \n",
-       "1  106302        5       0        2       0  \n",
-       "2   24632        1       0        1       0  \n",
-       "3   10553        0       0        0       0  "
+       "0  173183        6       0        3       0  \n",
+       "1   45412        2       0        0       0  \n",
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-       "<spot.impl.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7f7b0cb8dde0> >"
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-       "      <td>3899</td>\n",
-       "      <td>258963</td>\n",
-       "      <td>10</td>\n",
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+       "      <td>173427</td>\n",
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-       "      <td>3899</td>\n",
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        "      <td>6</td>\n",
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-       "2            6             4                4    11          32      3899   \n",
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+       "1            6             3              NaN   NaN         NaN      2747   \n",
+       "2            6             4                4    12          32      2747   \n",
        "\n",
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       ],
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-       "2            5             4                4    10          32      3894   \n",
-       "3            4             3              NaN   NaN         NaN       363   \n",
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        "\n",
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@@ -2972,122 +2916,136 @@
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-       "<spot.impl.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7f7b0cb610f0> >"
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        "      <th>0</th>\n",
        "      <td>6</td>\n",
        "      <td>6</td>\n",
-       "      <td>6</td>\n",
-       "      <td>19</td>\n",
-       "      <td>48</td>\n",
-       "      <td>3894</td>\n",
-       "      <td>258719</td>\n",
-       "      <td>10</td>\n",
-       "      <td>0</td>\n",
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-       "      <td>0</td>\n",
-       "      <td>HOA: v1 States: 6 Start: 0 AP: 3 \"a\" \"c\" \"b\" a...</td>\n",
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-       "    <tr>\n",
-       "      <th>1</th>\n",
-       "      <td>6</td>\n",
-       "      <td>5</td>\n",
-       "      <td>5</td>\n",
-       "      <td>14</td>\n",
+       "      <td>13</td>\n",
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-       "      <td>258767</td>\n",
-       "      <td>0</td>\n",
-       "      <td>0</td>\n",
+       "      <td>2742</td>\n",
+       "      <td>173183</td>\n",
+       "      <td>7</td>\n",
        "      <td>0</td>\n",
+       "      <td>3</td>\n",
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        "    </tr>\n",
        "    <tr>\n",
-       "      <th>2</th>\n",
+       "      <th>1</th>\n",
        "      <td>5</td>\n",
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        "      <td>4</td>\n",
-       "      <td>10</td>\n",
+       "      <td>12</td>\n",
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-       "      <td>258815</td>\n",
-       "      <td>0</td>\n",
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        "    <tr>\n",
-       "      <th>3</th>\n",
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-       "      <td>363</td>\n",
-       "      <td>10325</td>\n",
+       "      <td>2742</td>\n",
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       ],
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        "  input.states target.states reachable.states edges transitions variables  \\\n",
-       "0            6             6                6    19          48      3894   \n",
-       "1            6             5                5    14          40      3894   \n",
-       "2            5             4                4    10          32      3894   \n",
-       "3            4             3              NaN   NaN         NaN       363   \n",
+       "0            6             6                5    13          40      2742   \n",
+       "1            5             4                4    12          32      2742   \n",
+       "2            4             3              NaN   NaN         NaN      2742   \n",
        "\n",
        "  clauses enc.user enc.sys sat.user sat.sys  \\\n",
-       "0  258719       10       0        5       0   \n",
-       "1  258767        0       0        0       0   \n",
-       "2  258815        0       0        0       0   \n",
-       "3   10325        0       0        1       0   \n",
+       "0  173183        7       0        3       0   \n",
+       "1  173279        0       0        1       0   \n",
+       "2  173327        0       0        0       0   \n",
        "\n",
        "                                           automaton  \n",
-       "0  HOA: v1 States: 6 Start: 0 AP: 3 \"a\" \"c\" \"b\" a...  \n",
-       "1  HOA: v1 States: 5 Start: 0 AP: 3 \"a\" \"c\" \"b\" a...  \n",
-       "2  HOA: v1 States: 4 Start: 0 AP: 3 \"a\" \"c\" \"b\" a...  \n",
-       "3                                                NaN  "
+       "0  HOA: v1 States: 5 Start: 0 AP: 3 \"a\" \"c\" \"b\" a...  \n",
+       "1  HOA: v1 States: 4 Start: 0 AP: 3 \"a\" \"c\" \"b\" a...  \n",
+       "2                                                NaN  "
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+       "<text text-anchor=\"start\" x=\"257.7401\" y=\"-44.0148\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
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-       "<!-- 2&#45;&gt;1 -->\n",
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-       "<title>2&#45;&gt;1</title>\n",
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-       "<text text-anchor=\"start\" x=\"780.2203\" y=\"-131.8799\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">c | (a &amp; b)</text>\n",
+       "<!-- 0&#45;&gt;1 -->\n",
+       "<g id=\"edge3\" class=\"edge\">\n",
+       "<title>0&#45;&gt;1</title>\n",
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-       "<!-- 5 -->\n",
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-       "<title>5</title>\n",
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-       "<text text-anchor=\"middle\" x=\"809.2203\" y=\"-42.3799\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">5</text>\n",
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+       "<title>2</title>\n",
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+       "<text text-anchor=\"middle\" x=\"265.7401\" y=\"-114.5148\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">2</text>\n",
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-       "<!-- 2&#45;&gt;5 -->\n",
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-       "<title>2&#45;&gt;5</title>\n",
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-       "<!-- 4&#45;&gt;0 -->\n",
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-       "<title>4&#45;&gt;0</title>\n",
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-       "<!-- 4&#45;&gt;2 -->\n",
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-       "<title>4&#45;&gt;2</title>\n",
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-       "<title>4&#45;&gt;4</title>\n",
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-       "<title>4&#45;&gt;5</title>\n",
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-       "<text text-anchor=\"start\" x=\"508.4802\" y=\"-12.8799\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">a &amp; b &amp; c</text>\n",
+       "<!-- 0&#45;&gt;2 -->\n",
+       "<g id=\"edge4\" class=\"edge\">\n",
+       "<title>0&#45;&gt;2</title>\n",
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        "<!-- 3 -->\n",
-       "<g id=\"node7\" class=\"node\">\n",
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+       "<text text-anchor=\"middle\" x=\"553.7401\" y=\"-118.5148\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">3</text>\n",
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-       "<title>1&#45;&gt;2</title>\n",
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-       "<!-- 1&#45;&gt;1 -->\n",
+       "<!-- 0&#45;&gt;3 -->\n",
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-       "<title>1&#45;&gt;1</title>\n",
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+       "<title>0&#45;&gt;3</title>\n",
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+       "<!-- 4 -->\n",
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+       "<title>4</title>\n",
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+       "<g id=\"edge6\" class=\"edge\">\n",
+       "<title>0&#45;&gt;4</title>\n",
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+       "<title>1&#45;&gt;4</title>\n",
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+       "<!-- 2&#45;&gt;2 -->\n",
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-       "<!-- 3&#45;&gt;4 -->\n",
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+       "<title>2&#45;&gt;3</title>\n",
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-       "<spot.impl.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7f7b0cb61480> >"
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        "      <td>NaN</td>\n",
        "      <td>NaN</td>\n",
        "      <td>NaN</td>\n",
-       "      <td>975</td>\n",
-       "      <td>32912</td>\n",
+       "      <td>687</td>\n",
+       "      <td>21896</td>\n",
        "      <td>1</td>\n",
        "      <td>0</td>\n",
-       "      <td>1</td>\n",
+       "      <td>0</td>\n",
        "      <td>0</td>\n",
        "    </tr>\n",
        "    <tr>\n",
@@ -4061,13 +3794,13 @@
        "      <td>6</td>\n",
        "      <td>5</td>\n",
        "      <td>4</td>\n",
-       "      <td>10</td>\n",
+       "      <td>12</td>\n",
        "      <td>32</td>\n",
-       "      <td>2705</td>\n",
-       "      <td>150257</td>\n",
-       "      <td>6</td>\n",
+       "      <td>1905</td>\n",
+       "      <td>100457</td>\n",
+       "      <td>4</td>\n",
        "      <td>0</td>\n",
-       "      <td>3</td>\n",
+       "      <td>2</td>\n",
        "      <td>0</td>\n",
        "    </tr>\n",
        "  </tbody>\n",
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       ],
       "text/plain": [
        "  input.states target.states reachable.states edges transitions variables  \\\n",
-       "0            6             3              NaN   NaN         NaN       975   \n",
-       "1            6             5                4    10          32      2705   \n",
+       "0            6             3              NaN   NaN         NaN       687   \n",
+       "1            6             5                4    12          32      1905   \n",
        "\n",
        "  clauses enc.user enc.sys sat.user sat.sys  \n",
-       "0   32912        1       0        1       0  \n",
-       "1  150257        6       0        3       0  "
+       "0   21896        1       0        0       0  \n",
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-       "      <td>77340</td>\n",
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-       "0            6             4                4    12          32      1732   \n",
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        "  input.states target.states reachable.states edges transitions variables  \\\n",
-       "0            2             7                5    14          40      1869   \n",
+       "0            2             7                7    22          56      1379   \n",
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-       "<title>4&#45;&gt;3</title>\n",
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+       "<g id=\"edge17\" class=\"edge\">\n",
+       "<title>4&#45;&gt;1</title>\n",
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        "<!-- 4&#45;&gt;4 -->\n",
-       "<g id=\"edge15\" class=\"edge\">\n",
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+       "<title>5&#45;&gt;4</title>\n",
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+       "<!-- 5&#45;&gt;5 -->\n",
+       "<g id=\"edge21\" class=\"edge\">\n",
+       "<title>5&#45;&gt;5</title>\n",
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+       "</g>\n",
+       "<!-- 3 -->\n",
+       "<g id=\"node8\" class=\"node\">\n",
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+       "</g>\n",
+       "<!-- 5&#45;&gt;3 -->\n",
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+       "</g>\n",
+       "<!-- 6&#45;&gt;1 -->\n",
+       "<g id=\"edge22\" class=\"edge\">\n",
+       "<title>6&#45;&gt;1</title>\n",
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+       "</g>\n",
+       "<!-- 6&#45;&gt;6 -->\n",
+       "<g id=\"edge23\" class=\"edge\">\n",
+       "<title>6&#45;&gt;6</title>\n",
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+       "<!-- 3&#45;&gt;5 -->\n",
+       "<g id=\"edge15\" class=\"edge\">\n",
+       "<title>3&#45;&gt;5</title>\n",
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+       "<!-- 3&#45;&gt;6 -->\n",
+       "<g id=\"edge16\" class=\"edge\">\n",
+       "<title>3&#45;&gt;6</title>\n",
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+       "<!-- 3&#45;&gt;3 -->\n",
+       "<g id=\"edge13\" class=\"edge\">\n",
+       "<title>3&#45;&gt;3</title>\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 0x7f7b0cb61660> >"
+       "<spot.impl.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7f79cdae5270> >"
       ]
      },
      "execution_count": 21,
@@ -4724,6 +4540,13 @@
    "source": [
     "spot.sat_minimize(small, acc=\"co-Buchi\", states=7, state_based=True, display_log=True)"
    ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": []
   }
  ],
  "metadata": {
@@ -4742,7 +4565,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.6.5"
+   "version": "3.6.5+"
   }
  },
  "nbformat": 4,