reduce_parity: add layered option

* spot/twaalgos/parity.cc: Implement it.
* spot/twaalgos/parity.hh, NEWS: Document it.
* tests/python/parity.ipynb: Demonstrate it.  This is the only test so
far, but more uses are coming.

NEWS

@@ -1,5 +1,11 @@
 New in spot 2.11.1.dev  (not yet released)
 
+  Library:
+
+  - spot::reduce_parity() now has a "layered" option to force all
+    transition in the same parity layer to receive the same color;
+    like acd_transform() would do.
+
   Bugs fixed:
 
   - Fix pkg-config files containing @LIBSPOT_PTHREAD@ (issue #520)

spot/twaalgos/parity.cc

@@ -388,14 +388,14 @@ namespace spot
   }
 
   twa_graph_ptr
-  reduce_parity(const const_twa_graph_ptr& aut, bool colored)
+  reduce_parity(const const_twa_graph_ptr& aut, bool colored, bool layered)
   {
     return reduce_parity_here(make_twa_graph(aut, twa::prop_set::all()),
-                              colored);
+                              colored, layered);
   }
 
   twa_graph_ptr
-  reduce_parity_here(twa_graph_ptr aut, bool colored)
+  reduce_parity_here(twa_graph_ptr aut, bool colored, bool layered)
   {
     unsigned num_sets = aut->num_sets();
     if (!colored && num_sets == 0)
@@ -507,15 +507,30 @@ namespace spot
                   m.first += (piri - m.first) & 1;
                   m.second += (piri - m.second) & 1;
                 }
-              for (unsigned state: si.states_of(scc))
+              // Recolor edges.  Depending on LAYERED we want to
-                for (auto& e: aut->out(state))
+              // either recolor all edges for which piprime1 is -2
-                  if ((sba || si.scc_of(e.dst) == scc) &&
+              // (uncolored), or only the edges that we were removed
-                      ((piri >= 0 && e.acc.has(color)) || (piri < 0 && !e.acc)))
+              // by the previous filter.
-                    {
+              auto coloredge = [&](auto& e) {
                 unsigned en = aut->edge_number(e);
+                bool recolor = layered
+                  ? piprime1[en] == -2
+                  : (piri >= 0 && e.acc.has(color)) || (piri < 0 && !e.acc);
+                if (recolor)
+                  {
                     piprime1[en] = m.first;
                     piprime2[en] = m.second;
                   }
+              };
+              if (sba)
+                // si.edges_of(scc) would be wrong as it can ignore
+                // outgoing edges removed from a previous level.
+                for (unsigned s: si.states_of(scc))
+                  for (auto& e: aut->out(s))
+                    coloredge(e);
+              else
+                for (auto& e: si.inner_edges_of(scc))
+                  coloredge(e);
               res.first = std::max(res.first, m.first);
               res.second = std::max(res.second, m.second);
             }

spot/twaalgos/parity.hh

@@ -1,5 +1,5 @@
 // -*- coding: utf-8 -*-
-// Copyright (C) 2016-2019 Laboratoire de Recherche et Développement
+// Copyright (C) 2016-2019, 2022 Laboratoire de Recherche et Développement
 // de l'Epita (LRDE).
 //
 // This file is part of Spot, a model checking library.
@@ -134,7 +134,6 @@ namespace spot
   colorize_parity_here(twa_graph_ptr aut, bool keep_style = false);
   /// @}
 
-
   /// \brief Reduce the parity acceptance condition to use a minimal
   /// number of colors.
   ///
@@ -149,11 +148,51 @@ namespace spot
   /// the above paper assumes).  Otherwise, the smallest or highest
   /// colors (depending on the parity kind) is removed to simplify the
   /// acceptance condition.
+  ///
+  /// If the input uses state-based acceptance, the output will use
+  /// state-based acceptance as well.
+  ///
+  /// A parity automaton, sometimes called a chain automaton, can be
+  /// seen as a stack of layers that are alternatively rejecting and
+  /// accepting.  For instance imagine a parity max automaton that is
+  /// strongly connected.  Removing the transitions with the maximal
+  /// color might leave a few transitions that were not labeled by
+  /// this maximal color, but that are part of any cycle anymore:
+  /// those transition could have been colored with the maximal color,
+  /// since any cycle going through them would have seen the maximal
+  /// color.  (Once your remove this maximal layer,
+  /// your can define the next layer similarly.)
+  ///
+  /// When \a layered is true all transition that belong to the same
+  /// layer receive the same color.  When layer is `false`, only the
+  /// transition that where used initially to define the layers (i.e,
+  /// the transition with the maximal color in the previous exemple),
+  /// get their color adjusted.  The other will receive either no
+  /// color (if \a colored is false), or a useless color (if \a colored
+  /// is true).  Here "useless color" means the smallest color
+  /// for parity max, and the largest color for parity min.
+  ///
+  /// When \a layered is true, the output of this function is
+  /// comparable to what acd_transform() would produce.  The
+  /// difference is that this function preserve the kind (min/max) of
+  /// parity input, while acd_transform() always output a parity min
+  /// automaton.  Additionally, this function needs fewer resources
+  /// than acd_transform() because it is already known that the input
+  /// is a parity automaton.  In some (historically inaccurate) way,
+  /// reduce_parity() can be seen as a specialized version of
+  /// acd_transform().
+  ///
+  /// The reason layered is false by default, is that not introducing
+  /// colors in place where there where none occasionally help with
+  /// simulation-based reductions.
+  ///
   /// @{
   SPOT_API twa_graph_ptr
-  reduce_parity(const const_twa_graph_ptr& aut, bool colored = false);
+  reduce_parity(const const_twa_graph_ptr& aut,
+                bool colored = false, bool layered = false);
 
   SPOT_API twa_graph_ptr
-  reduce_parity_here(twa_graph_ptr aut, bool colored = false);
+  reduce_parity_here(twa_graph_ptr aut,
+                     bool colored = false, bool layered = false);
   /// @}
 }

tests/python/parity.ipynb

@@ -72,9 +72,9 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "Of course the case of parity automata with a single color is a bit degenerate, as the same formula correspond to two parity conditions with different kinds. \n",
+    "Of course the case of parity automata with a single color is a bit degenerate, as the same formula corresponds to two parity conditions of different kinds. \n",
     "\n",
-    "In addition the the above, an automaton is said to be **colored** if each of its edges (or states) has exactly one color.  Automata that people usually call *parity automata* correspond in Spot to *colored* automata with *parity acceptance*.  For this reason try to use the term *automata with parity acceptance* rather than *parity automata* for automata that are not *colored*."
+    "In addition to the above, an automaton is said to be **colored** if each of its edges (or states) has exactly one color.  Automata that people usually call *parity automata* correspond in Spot to *colored* automata with *parity acceptance*.  For this reason try to use the term *automata with parity acceptance* rather than *parity automata* for automata that are not *colored*."
    ]
   },
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@@ -4223,14 +4223,15 @@
     "\n",
     "# Reduce parity\n",
     "\n",
-    "The `reduce_parity()` function is a more elaborate version of `cleanup_parity()`.  It implements an algorithm by Carton and Maceiras (*Computing the Rabin index of a parity automaton*, Informatique théorique et applications, 1999), to obtain the minimal parity acceptance condition for a given automaton.  Why the original algorithm assume *max odd* parity, this version with work with the four types of parity acceptance.  It will only try to preserve the kind (max/min) and may change the style if it allows saving one color.  Furthermore, it can colorize (or uncolorize) automata at the same time,\n",
+    "The `reduce_parity()` function is a more elaborate version of `cleanup_parity()`.  It implements an algorithm by Carton and Maceiras (*Computing the Rabin index of a parity automaton*, Informatique théorique et applications, 1999), to obtain the minimal parity acceptance condition for a given automaton.  While the original algorithm assumes *max odd* parity, this version works with the four types of parity acceptance.  It will only try to preserve the kind (max/min) and may change the style if it allows saving one color.  Furthermore, it can colorize (or uncolorize) automata at the same time,\n",
     "making it a very nice replacement for both `cleanup_parity()` and `colorize_parity()`.\n",
     "\n",
-    "It takes two arguments:\n",
+    "It takes three arguments:\n",
     "1. the automaton whose parity acceptance condition should be reduced\n",
     "2. a Boolean indicating whether the output should be colored (`True`), or if transition with no color can be used (`False`).\n",
+    "3. a Boolean indicating whether the output should be layered, i.e., in a max parity automaton, that means the color of a transition should be the maximal color visited by all cycles going through it.\n",
     "\n",
-    "By default, the second argument is `False`, because acceptance sets is a scarse ressource in Spot."
+    "By default, the second argument is `False`, because acceptance sets is a scarse ressource in Spot.  The third argument also defaults to `False`, but for empircal reason: adding more colors like this tends to hinder simulation-based reductions."
    ]
   },
   {
@@ -4715,8 +4716,8 @@
    "outputs": [
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+       "<path fill=\"none\" stroke=\"black\" d=\"M213.36,-34.8C237.59,-40.26 282.36,-50.36 310.02,-56.59\"/>\n",
+       "<polygon fill=\"black\" stroke=\"black\" points=\"317,-58.17 309.48,-59.7 313.59,-57.4 310.17,-56.63 310.17,-56.63 310.17,-56.63 313.59,-57.4 310.87,-53.56 317,-58.17 317,-58.17\"/>\n",
+       "<text text-anchor=\"start\" x=\"242\" y=\"-71.8\" font-family=\"Lato\" font-size=\"14.00\">!p0 &amp; !p1</text>\n",
+       "<text text-anchor=\"start\" x=\"262.5\" y=\"-56.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff7f00\">❷</text>\n",
+       "</g>\n",
+       "<!-- 3&#45;&gt;3 -->\n",
+       "<g id=\"edge9\" class=\"edge\">\n",
+       "<title>3&#45;&gt;3</title>\n",
+       "<path fill=\"none\" stroke=\"black\" d=\"M183.58,-44.67C178.81,-55.66 182.78,-67 195.5,-67 205.44,-67 210.04,-60.08 209.3,-51.81\"/>\n",
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+       "<text text-anchor=\"start\" x=\"169\" y=\"-85.8\" font-family=\"Lato\" font-size=\"14.00\">!p0 &amp; p1</text>\n",
+       "<text text-anchor=\"start\" x=\"187.5\" y=\"-70.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff4da0\">❶</text>\n",
+       "</g>\n",
+       "<!-- 1&#45;&gt;0 -->\n",
+       "<g id=\"edge4\" class=\"edge\">\n",
+       "<title>1&#45;&gt;0</title>\n",
+       "<path fill=\"none\" stroke=\"black\" d=\"M447.25,-11.4C441.33,-9.24 434.46,-7.11 428,-6 377.52,2.67 236.49,-0.76 167,-4 133.56,-5.56 121.91,4.05 92,-11 83.75,-15.15 76.53,-22.15 70.83,-29.08\"/>\n",
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+       "<text text-anchor=\"start\" x=\"244\" y=\"-19.8\" font-family=\"Lato\" font-size=\"14.00\">!p0 &amp; p1</text>\n",
+       "<text text-anchor=\"start\" x=\"262.5\" y=\"-4.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff4da0\">❶</text>\n",
+       "</g>\n",
+       "<!-- 1&#45;&gt;2 -->\n",
+       "<g id=\"edge5\" class=\"edge\">\n",
+       "<title>1&#45;&gt;2</title>\n",
+       "<path fill=\"none\" stroke=\"black\" d=\"M446.09,-14.08C426.86,-10.52 395.03,-7.42 371,-19 361.6,-23.53 353.89,-31.93 348.12,-40.11\"/>\n",
+       "<polygon fill=\"black\" stroke=\"black\" points=\"344.09,-46.26 345.29,-38.68 346.01,-43.33 347.93,-40.41 347.93,-40.41 347.93,-40.41 346.01,-43.33 350.56,-42.13 344.09,-46.26 344.09,-46.26\"/>\n",
+       "<text text-anchor=\"start\" x=\"371\" y=\"-37.8\" font-family=\"Lato\" font-size=\"14.00\">!p0 &amp; !p1</text>\n",
+       "<text text-anchor=\"start\" x=\"391.5\" y=\"-22.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
+       "</g>\n",
+       "</g>\n",
+       "</svg>\n",
+       "</div>"
+      ],
+      "text/plain": [
+       "<IPython.core.display.HTML object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
     }
    ],
    "source": [
-    "display2(maxeven4, spot.reduce_parity(maxeven4))\n",
+    "display(maxeven4)\n",
-    "display2(maxeven4, spot.reduce_parity(maxeven4, True))"
+    "display2(spot.reduce_parity(maxeven4), spot.reduce_parity(maxeven4, True))\n",
+    "display2(spot.reduce_parity(maxeven4, False, True), spot.reduce_parity(maxeven4, True, True))"
    ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": []
   }
  ],
  "metadata": {
   "kernelspec": {
-   "display_name": "Python 3",
+   "display_name": "Python 3 (ipykernel)",
    "language": "python",
    "name": "python3"
   },
@@ -5212,7 +5344,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.8.2"
+   "version": "3.10.7"
   }
  },
  "nbformat": 4,