introduce a zielonka_tree class

* spot/twaalgos/zlktree.cc, spot/twaalgos/zlktree.hh: New files.
* spot/twaalgos/Makefile.am: Add them.
* tests/python/_zlktree.ipynb: New file.
* tests/Makefile.am: Add it.
* python/spot/__init__.py, python/spot/impl.i: Add bindings for it.
* doc/spot.bib (casares.21.icalp): New entry.
* NEWS: Mention this.

spot/twaalgos/zlktree.hh

@@ -0,0 +1,132 @@
+// -*- coding: utf-8 -*-
+// Copyright (C) 2021 Laboratoire de Recherche et Developpement de
+// l'Epita (LRDE).
+//
+// This file is part of Spot, a model checking library.
+//
+// Spot is free software; you can redistribute it and/or modify it
+// under the terms of the GNU General Public License as published by
+// the Free Software Foundation; either version 3 of the License, or
+// (at your option) any later version.
+//
+// Spot is distributed in the hope that it will be useful, but WITHOUT
+// ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
+// or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public
+// License for more details.
+//
+// You should have received a copy of the GNU General Public License
+// along with this program.  If not, see <http://www.gnu.org/licenses/>.
+
+#pragma once
+
+#include <iosfwd>
+#include <spot/twa/twagraph.hh>
+
+namespace spot
+{
+  /// \ingroup twa_acc_transform
+  /// \brief Zielonka Tree implementation
+  ///
+  /// This class implements a Zielonka Tree, using
+  /// conventions similar to those in \cite casares.21.icalp
+  ///
+  /// The differences is that this tree is built from Emerson-Lei
+  /// acceptance conditions, and can be "walked through" with multiple
+  /// colors at once.
+  class SPOT_API zielonka_tree
+  {
+  public:
+    /// \brief Build a Zielonka tree from the acceptance condition.
+    zielonka_tree(acc_cond& cond);
+
+    /// \brief The number of branches in the Zielonka tree.
+    ///
+    /// Branch are designated by the node number of their
+    /// leaves.
+    unsigned num_branches() const
+    {
+      return num_branches_;
+    }
+
+    /// \brief The number of one branch in the tree.
+    ///
+    /// This returns the branch whose leave is the smallest one.
+    unsigned first_branch() const
+    {
+      return one_branch_;
+    }
+
+    /// \brief Walk through the Zielonka tree.
+    ///
+    /// Given a \a branch number, and a set of \a colors, this returns
+    /// a pair (new branch, level), as needed in definition 3.7 of
+    /// \cite casares.21.icalp
+    ///
+    /// The level correspond to the priority of a minimum parity acceptance
+    /// condition, with the parity odd/even as specified by is_even().
+    ///
+    /// This implementation is slightly different from the original
+    /// definition since it allows a set of colors to be processed,
+    /// and not exactly one color.  When multiple colors are given,
+    /// the minimum corresponding level is returned.  When no color is
+    /// given, the branch is not changed and the level returned is one
+    /// more than the depth of that branch (this is as if the tree add
+    /// another layer of leaves labeled by the empty sets, that do not
+    /// store for simplicity).
+    std::pair<unsigned, unsigned>
+    step(unsigned branch, acc_cond::mark_t colors) const;
+
+    /// \brief Whether the tree corresponds to a min even or min odd
+    /// parity acceptance.
+    bool is_even() const
+    {
+      return is_even_;
+    }
+
+    /// \brief Whether the Zielonka tree has Rabin shape.
+    ///
+    /// The tree has Rabin shape of all accepting (round) nodes have
+    /// at most one child.
+    bool has_rabin_shape() const
+    {
+      return has_rabin_shape_;
+    }
+
+    /// \brief Whether the Zielonka tree has Streett shape.
+    ///
+    /// The tree has Streett shape of all rejecting (square) nodes have
+    /// at most one child.
+    bool has_streett_shape() const
+    {
+      return has_streett_shape_;
+    }
+
+    /// \brief Whether the Zielonka tree has parity shape.
+    ///
+    /// The tree has parity shape of all nodes have at most one child.
+    bool has_parity_shape() const
+    {
+      return has_streett_shape_ && has_rabin_shape_;
+    }
+
+    /// \brief Render the tree as in GraphViz format.
+    void dot(std::ostream&) const;
+
+  private:
+    struct zielonka_node
+    {
+      unsigned parent;
+      unsigned next_sibling = 0;
+      unsigned first_child = 0;
+      unsigned level;
+      acc_cond::mark_t colors;
+    };
+    std::vector<zielonka_node> nodes_;
+    unsigned one_branch_ = 0;
+    unsigned num_branches_ = 0;
+    bool is_even_;
+    bool has_rabin_shape_ = true;
+    bool has_streett_shape_ = true;
+  };
+
+}