spot/spot/twaalgos/determinize.cc

// -*- coding: utf-8 -*-
// Copyright (C) 2015-2017 Laboratoire de Recherche et
// Développement de l'Epita.
//
// 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/>.

#include <algorithm>
#include <deque>
#include <stack>
#include <utility>
#include <unordered_map>
#include <set>
#include <map>


#include <spot/misc/bddlt.hh>
#include <spot/twaalgos/sccinfo.hh>
#include <spot/twaalgos/determinize.hh>
#include <spot/twaalgos/degen.hh>
#include <spot/twaalgos/sccfilter.hh>
#include <spot/twaalgos/simulation.hh>
#include <spot/twaalgos/isdet.hh>


namespace spot
{
  namespace
  {
    // forward declaration
    struct safra_build;
  }

  class safra_state final
  {
  public:
    // a helper method to check invariants
    void
    check() const
    {
      // do not refer to braces that do not exist
      for (const auto& p : nodes_)
        if (p.second >= 0)
          if (((unsigned)p.second) >= braces_.size())
            assert(false);

      // braces_ describes the parenthood relation, -1 meaning toplevel
      // so braces_[b] < b always, and -1 is the only negative number allowed
      for (int b : braces_)
        {
          if (b < 0 && b != -1)
            assert(false);
          if (b >= 0 && braces_[b] > b)
            assert(false);
        }

      // no unused braces
      std::set<int> used_braces;
      for (const auto& n : nodes_)
        {
          int b = n.second;
          while (b >= 0)
            {
              used_braces.insert(b);
              b = braces_[b];
            }
        }
      assert(used_braces.size() == braces_.size());
    }

  public:
    using state_t = unsigned;
    using safra_node_t = std::pair<state_t, std::vector<int>>;

    bool operator<(const safra_state&) const;
    bool operator==(const safra_state&) const;
    size_t hash() const;

    // Print the number of states in each brace
    // default constructor
    safra_state(): safra_state(0) {}
    safra_state(state_t state_number, bool acceptance_scc = false);
    safra_state(safra_build&& s, unsigned c);
    // Compute successor for transition ap
    safra_state
    compute_succ(const const_twa_graph_ptr& aut,
                 const bdd& ap,
                 const scc_info& scc,
                 const std::vector<bdd>& implications,
                 const std::vector<char>& is_connected,
                 bool use_scc,
                 bool use_simulation) const;

    // each brace points to its parent.
    // braces_[i] is the parent of i
    // Note that braces_[i] < i, -1 stands for "no parent" (top-level)
    std::vector<int> braces_;
    std::vector<std::pair<state_t, int>> nodes_;
    // FIXME this does not belong to the safra_state
    unsigned color_;
  };

  namespace
  {
    struct hash_safra
    {
      size_t
      operator()(const safra_state& s) const
      {
        return s.hash();
      }
    };

    template<class T>
    struct ref_wrap_equal
    {
      bool
      operator()(const std::reference_wrapper<T>& x,
                 const std::reference_wrapper<T>& y) const
      {
        return std::equal_to<T>()(x.get(), y.get());
      }
    };

    using power_set = std::unordered_map<safra_state, unsigned, hash_safra>;

    std::string
    nodes_to_string(const const_twa_graph_ptr& aut,
                    const safra_state& states);

    // Given a certain transition_label, compute all the successors of a
    // safra_state under that label, and return the new nodes in res.
    class compute_succs final
    {
      const safra_state& src;
      const const_twa_graph_ptr& aut;
      const power_set& seen;
      const scc_info& scc;
      const std::vector<bdd>& implications;
      const std::vector<char>& is_connected;
      const std::vector<bdd>& all_bdds;
      bool use_scc;
      bool use_simulation;
      bool use_stutter;

      // to iterate on successors
      std::vector<bdd>::const_iterator bddit;
      safra_state ss;
    public:
      compute_succs(const safra_state& src,
                    const const_twa_graph_ptr& aut,
                    const power_set& seen,
                    const scc_info& scc,
                    const std::vector<bdd>& implications,
                    const std::vector<char>& is_connected,
                    const std::vector<bdd>& all_bdds,
                    bool use_scc,
                    bool use_simulation,
                    bool use_stutter)
      : src(src)
      , aut(aut)
      , seen(seen)
      , scc(scc)
      , implications(implications)
      , is_connected(is_connected)
      , all_bdds(all_bdds)
      , use_scc(use_scc)
      , use_simulation(use_simulation)
      , use_stutter(use_stutter)
      {}

      struct iterator
      {
        const compute_succs& cs_;
        std::vector<bdd>::const_iterator bddit;
        safra_state ss;

        iterator(const compute_succs& c, std::vector<bdd>::const_iterator it)
        : cs_(c)
        , bddit(it)
        {
          compute_();
        }

        bool
        operator!=(const iterator& other) const
        {
          return bddit != other.bddit;
        }

        iterator&
        operator++()
        {
          ++bddit;
          compute_();
          return *this;
        }
        // no need to implement postfix increment

        bdd
        cond() const
        {
          return *bddit;
        }

        const safra_state&
        operator*() const
        {
          return ss;
        }
        const safra_state*
        operator->() const
        {
          return &ss;
        }

      private:
        void
        compute_()
        {
          if (bddit == cs_.all_bdds.end())
            return;

          const bdd& ap = *bddit;
          ss = cs_.src;

          if (cs_.use_stutter && cs_.aut->prop_stutter_invariant())
            {
              bool stop = false;
              std::deque<safra_state> path;
              std::unordered_set<
                std::reference_wrapper<const safra_state>,
                hash_safra,
                ref_wrap_equal<const safra_state>> states;
              unsigned mincolor = -1U;
              while (!stop)
                {
                  path.emplace_back(std::move(ss));
                  auto i = states.insert(path.back());
                  assert(i.second);
                  ss = path.back().compute_succ(cs_.aut, ap, cs_.scc,
                                                cs_.implications,
                                                cs_.is_connected, cs_.use_scc,
                                                cs_.use_simulation);
                  mincolor = std::min(ss.color_, mincolor);
                  stop = states.find(ss) != states.end();
                }

              // also insert last element (/!\ it thus appears twice in path)
              path.emplace_back(std::move(ss));
              const safra_state& loopstart = path.back();
              bool in_seen = cs_.seen.find(ss) != cs_.seen.end();
              unsigned tokeep = path.size()-1;
              unsigned idx = path.size()-2;
              // The loop is guaranteed to end, because path contains too
              // occurrences of loopstart
              while (!(loopstart == path[idx]))
                {
                  // if path[tokeep] is already in seen, replace it with a
                  // smaller state also in seen.
                  if (in_seen && cs_.seen.find(path[idx]) != cs_.seen.end())
                    if (path[idx] < path[tokeep])
                      tokeep = idx;

                  // if path[tokeep] is not in seen, replace it either with a
                  // state in seen or with a smaller state
                  if (!in_seen)
                    {
                      if (cs_.seen.find(path[idx]) != cs_.seen.end())
                        {
                          tokeep = idx;
                          in_seen = true;
                        }
                      else if (path[idx] < path[tokeep])
                        tokeep = idx;
                    }
                  --idx;
                }
              // clean references to path before move (see next line)
              states.clear();
              // move is safe, no dangling references
              ss = std::move(path[tokeep]);
              ss.color_ = mincolor;
            }
          else
            ss = cs_.src.compute_succ(cs_.aut, ap, cs_.scc, cs_.implications,
                                      cs_.is_connected, cs_.use_scc,
                                      cs_.use_simulation);
        }
      };

      iterator
      begin() const
      {
        return iterator(*this, all_bdds.begin());
      }
      iterator
      end() const
      {
        return iterator(*this, all_bdds.end());
      }
    };

    const char* const sub[10] =
      {
        "\u2080",
        "\u2081",
        "\u2082",
        "\u2083",
        "\u2084",
        "\u2085",
        "\u2086",
        "\u2087",
        "\u2088",
        "\u2089",
      };

    std::string subscript(unsigned start)
    {
      std::string res;
      do
        {
          res = sub[start % 10] + res;
          start /= 10;
        }
      while (start);
      return res;
    }

    // Returns true if lhs has a smaller nesting pattern than rhs
    // If lhs and rhs are the same, return false.
    // NB the nesting patterns are backwards.
    bool nesting_cmp(const std::vector<int>& lhs,
                     const std::vector<int>& rhs)
    {
      unsigned m = std::min(lhs.size(), rhs.size());
      auto lit = lhs.rbegin();
      auto rit = rhs.rbegin();
      for (unsigned i = 0; i != m; ++i)
        {
          if (*lit != *rit)
            return *lit < *rit;
        }
      return lhs.size() > rhs.size();
    }

    // Used to remove all acceptance whose value is above or equal to max_acc
    void remove_dead_acc(twa_graph_ptr& aut, unsigned max_acc)
    {
      assert(max_acc < 32);
      unsigned mask = (1 << max_acc) - 1;
      for (auto& t: aut->edges())
        t.acc &= mask;
    }

    struct compare
    {
      bool
      operator() (const safra_state::safra_node_t& lhs,
                  const safra_state::safra_node_t& rhs)
      {
        return lhs.second < rhs.second;
      }
    };

    // Return the nodes sorted in ascending order
    std::vector<safra_state::safra_node_t>
    sorted_nodes(const safra_state& s)
    {
      std::vector<safra_state::safra_node_t> res;
      for (const auto& n: s.nodes_)
        {
          int brace = n.second;
          std::vector<int> tmp;
          while (brace >= 0)
            {
              // FIXME is not there a smarter way?
              tmp.insert(tmp.begin(), brace);
              brace = s.braces_[brace];
            }
          res.emplace_back(n.first, std::move(tmp));
        }
      std::sort(res.begin(), res.end(), compare());
      return res;
    }

    std::string
    nodes_to_string(const const_twa_graph_ptr& aut,
                    const safra_state& states)
    {
      auto copy = sorted_nodes(states);
      std::ostringstream os;
      std::stack<int> s;
      bool first = true;
      for (const auto& n: copy)
        {
          auto it = n.second.begin();
          // Find brace on top of stack in vector
          // If brace is not present, then we close it as no other ones of that
          // type will be found since we ordered our vector
          while (!s.empty())
            {
              it = std::lower_bound(n.second.begin(), n.second.end(),
                                    s.top());
              if (it == n.second.end() || *it != s.top())
                {
                  os << subscript(s.top()) << '}';
                  s.pop();
                }
              else
                {
                  if (*it == s.top())
                    ++it;
                  break;
                }
            }
          // Add new braces
          while (it != n.second.end())
            {
              os << '{' << subscript(*it);
              s.push(*it);
              ++it;
              first = true;
            }
          if (!first)
            os << ' ';
          os << aut->format_state(n.first);
          first = false;
        }
      // Finish unwinding stack to print last braces
      while (!s.empty())
        {
          os << subscript(s.top()) << '}';
          s.pop();
        }
      return os.str();
    }

    std::vector<std::string>*
    print_debug(const const_twa_graph_ptr& aut,
                const power_set& states)
    {
      auto res = new std::vector<std::string>(states.size());
      for (const auto& p: states)
        (*res)[p.second] = nodes_to_string(aut, p.first);
      return res;
    }

    // a helper class for building the successor of a safra_state
    struct safra_build final
    {
      std::vector<int> braces_;
      std::map<unsigned, int> nodes_;

      safra_build(const std::vector<int>& b)
      : braces_(b)
      {}

      bool
      compare_braces(int a, int b)
      {
        std::vector<int> a_pattern;
        std::vector<int> b_pattern;
        a_pattern.reserve(a+1);
        b_pattern.reserve(b+1);
        while (a != b)
          {
            if (a > b)
              {
                a_pattern.emplace_back(a);
                a = braces_[a];
              }
            else
              {
                b_pattern.emplace_back(b);
                b = braces_[b];
              }
          }
        return nesting_cmp(a_pattern, b_pattern);
      }

      // Used when creating the list of successors
      // A new intermediate node is created with src's braces and with dst as id
      // A merge is done if dst already existed in *this
      void
      update_succ(int brace, unsigned dst, const acc_cond::mark_t acc)
      {
        int newb = brace;
        if (acc.count())
          {
            assert(acc.has(0) && acc.count() == 1 && "Only TBA are accepted");
            // Accepting edges generate new braces: step A1
            newb = braces_.size();
            braces_.emplace_back(brace);
          }
        auto i = nodes_.emplace(dst, newb);
        if (!i.second) // dst already exists
          {
            // Step A2: Only keep the smallest nesting pattern.
            // Use nesting_cmp to compare nesting patterns.
            if (compare_braces(newb, i.first->second))
              {
                i.first->second = newb;
              }
            else
              {
                if (newb != brace) // new brace was created but is not needed
                  braces_.pop_back();
              }
          }
      }

      // When a node a implies a node b, remove the node a.
      void
      merge_redundant_states(const std::vector<bdd>& implications,
                             const scc_info& scc,
                             const std::vector<char>& is_connected)
      {
        std::vector<unsigned> to_remove;
        for (const auto& n1: nodes_)
          for (const auto& n2: nodes_)
            {
              if (n1 == n2)
                continue;
              // index to see if there is a path from scc2 -> scc1
              unsigned idx = scc.scc_count() * scc.scc_of(n2.first) +
                scc.scc_of(n1.first);
              if (!is_connected[idx] && bdd_implies(implications.at(n1.first),
                                                    implications.at(n2.first)))
                to_remove.emplace_back(n1.first);
            }
        for (unsigned n: to_remove)
          nodes_.erase(n);
      }

      // Return the emitted color, red or green
      unsigned
      finalize_construction()
      {
        unsigned red = -1U;
        unsigned green = -1U;
        // use std::vector<char> to avoid std::vector<bool>
        // a char encodes several bools:
        //  * first bit says whether the brace is empty and red
        //  * second bit says whether the brace is green
        // brackets removed from green pairs can be safely be marked as red,
        // because their enclosing green has a lower number
        // beware of pairs marked both as red and green: they are actually empty
        constexpr char is_empty = 1;
        constexpr char is_green = 2;
        std::vector<char> empty_green(braces_.size(), 3);

        for (const auto& n : nodes_)
          if (n.second >= 0)
            {
              int brace = n.second;
              // Step A4: For a brace to be green it must not contain states
              // on its own.
              empty_green[brace] &= ~is_green;
              while (brace >= 0 && (empty_green[brace] & is_empty))
                {
                  empty_green[brace] &= ~is_empty;
                  brace = braces_[brace];
                }
            }
        // Step A4 Remove brackets within green pairs
        // for each bracket, find its highest green ancestor
        // 0 cannot be in a green pair, its highest green ancestor is itself
        std::vector<unsigned> highest_green_ancestor(braces_.size(), 0);
        for (unsigned b = 0; b != braces_.size(); ++b)
          {
            highest_green_ancestor[b] = b;
            int ancestor = braces_[b];
            // Note that ancestor strictly decreases
            // FIXME is there a smarter way to do that?
            while (ancestor >= 0)
              {
                if (empty_green[ancestor] & is_green)
                  highest_green_ancestor[b] = ancestor;
                ancestor = braces_[ancestor];
              }
            if (highest_green_ancestor[b] != b)
              empty_green[b] |= is_empty; // mark brace for removal
          }
        for (auto& n : nodes_)
          if (n.second >= 0)
            n.second = highest_green_ancestor[n.second];

        // find red and green signals to emit
        // also compute the number of braces to remove for renumbering
        std::vector<unsigned> decr_by(braces_.size());
        unsigned decr = 0;
        for (unsigned i = 0; i != braces_.size(); ++i)
          {
            if (empty_green[i] & is_empty)
              {
                // Step A5 renumber braces
                ++decr;

                // Step A3 emit red
                red = std::min(red, 2*i);
              }
            else if (empty_green[i] & is_green)
              {
                // Step A4 emit green
                green = std::min(green, 2*i+1);
              }

            decr_by[i] = decr;
          }

        std::vector<int> new_braces(braces_.size() - decr);
        for (auto& n : nodes_)
          {
            if (n.second >= 0)
              {
                unsigned i = n.second;
                int j = braces_[i] >=0 ? braces_[i] - decr_by[braces_[i]] : -1;
                new_braces[i - decr_by[i]] = j;
                n.second = i - decr_by[i];
              }
          }
        std::swap(braces_, new_braces);

        return std::min(red, green);
      }

    };

    // Compute a vector of letters from a given support
    std::vector<bdd>
    letters(bdd allap)
    {
      std::vector<bdd> res;
      bdd all = bddtrue;
      while (all != bddfalse)
        {
          bdd one = bdd_satoneset(all, allap, bddfalse);
          all -= one;
          res.emplace_back(one);
        }
      return res;
    }

    class safra_support
    {
      const std::vector<bdd>& state_supports;
      std::unordered_map<bdd, std::vector<bdd>, bdd_hash> cache;

    public:
      safra_support(const std::vector<bdd>& s): state_supports(s) {}

      const std::vector<bdd>&
      get(const safra_state& s)
      {
        bdd supp = bddtrue;
        for (const auto& n : s.nodes_)
          supp &= state_supports[n.first];
        auto it = cache.find(supp);
        if (it == cache.end())
          it = cache.emplace(supp, letters(supp)).first;
        return it->second;
      }
    };
  }

  std::vector<char> find_scc_paths(const scc_info& scc);

  safra_state
  safra_state::compute_succ(const const_twa_graph_ptr& aut,
                            const bdd& ap,
                            const scc_info& scc,
                            const std::vector<bdd>& implications,
                            const std::vector<char>& is_connected,
                            bool use_scc,
                            bool use_simulation) const
  {
    // FIXME: we manipulate one safra_build at a time: how can we optimize/avoid
    // allocation/deallocation?
    safra_build ss(braces_);
    for (const auto& node: nodes_)
      {
        for (const auto& t: aut->out(node.first))
          {
            if (!bdd_implies(ap, t.cond))
              continue;
            // Check if we are leaving the SCC, if so we delete all the
            // braces as no cycles can be found with that node
            if (use_scc && scc.scc_of(node.first) != scc.scc_of(t.dst))
              if (scc.is_accepting_scc(scc.scc_of(t.dst)))
                // Entering accepting SCC so add brace
                ss.update_succ(-1, t.dst, { 0 });
              else
                // When entering non accepting SCC don't create any braces
                ss.update_succ(-1, t.dst, { /* empty */ });
            else
              ss.update_succ(node.second, t.dst, t.acc);
          }
      }
    if (use_simulation)
      ss.merge_redundant_states(implications, scc, is_connected);
    unsigned color = ss.finalize_construction();
    return safra_state(std::move(ss), color);
  }

  // Called only to initialize first state
  safra_state::safra_state(state_t val, bool accepting_scc)
  {
    if (!accepting_scc)
      {
        // -1 means "no braces"
        nodes_.emplace_back(val, -1);
      }
    else
      {
        braces_.emplace_back(-1);
        nodes_.emplace_back(val, 0);
      }
  }

  safra_state::safra_state(safra_build&& s, unsigned c)
  : braces_(std::move(s.braces_))
  , nodes_(std::make_move_iterator(s.nodes_.begin()),
           std::make_move_iterator(s.nodes_.end()))
  , color_(c)
  {}

  bool
  safra_state::operator<(const safra_state& other) const
  {
    // FIXME what is the right, if any, comparison to perform?
    return braces_ == other.braces_ ? nodes_ < other.nodes_
                                    : braces_ < other.braces_;
  }
  size_t
  safra_state::hash() const
  {
    size_t res = 0;
    for (const auto& p : nodes_)
      {
        res ^= (res << 3) ^ p.first;
        res ^= (res << 3) ^ p.second;
      }
    for (const auto& b : braces_)
      res ^= (res << 3) ^ b;
    return res;
  }

  bool
  safra_state::operator==(const safra_state& other) const
  {
    return nodes_ == other.nodes_ && braces_ == other.braces_;
  }

  // res[i + scccount*j] = 1 iff SCC i is reachable from SCC j
  std::vector<char>
  find_scc_paths(const scc_info& scc)
  {
    unsigned scccount = scc.scc_count();
    std::vector<char> res(scccount * scccount, 0);
    for (unsigned i = 0; i != scccount; ++i)
      res[i + scccount * i] = 1;
    for (unsigned i = 0; i != scccount; ++i)
      {
        std::stack<unsigned> s;
        s.push(i);
        while (!s.empty())
          {
            unsigned src = s.top();
            s.pop();
            for (unsigned d: scc.succ(src))
              {
                s.push(d);
                unsigned idx = scccount * i + d;
                res[idx] = 1;
              }
          }
      }
    return res;
  }

  twa_graph_ptr
  tgba_determinize(const const_twa_graph_ptr& a,
                   bool pretty_print, bool use_scc,
                   bool use_simulation, bool use_stutter)
  {
    if (!a->is_existential())
      throw std::runtime_error
        ("tgba_determinize() does not support alternation");
    if (is_universal(a))
      return std::const_pointer_cast<twa_graph>(a);

    // Degeneralize
    const_twa_graph_ptr aut;
    std::vector<bdd> implications;
    {
      twa_graph_ptr aut_tmp = spot::degeneralize_tba(a);
      if (pretty_print)
        aut_tmp->copy_state_names_from(a);
      if (use_simulation)
        {
          aut_tmp = spot::scc_filter(aut_tmp);
          auto aut2 = simulation(aut_tmp, &implications);
          if (pretty_print)
            aut2->copy_state_names_from(aut_tmp);
          aut_tmp = aut2;
        }
      aut = aut_tmp;
    }
    scc_info_options scc_opt = scc_info_options::TRACK_SUCCS;
    // We do need to track states in SCC for stutter invariance (see below how
    // supports are computed in this case)
    if (use_stutter && aut->prop_stutter_invariant())
      scc_opt = scc_info_options::TRACK_SUCCS | scc_info_options::TRACK_STATES;
    scc_info scc = scc_info(aut, scc_opt);
    std::vector<char> is_connected = find_scc_paths(scc);

    // Compute the support of each state
    std::vector<bdd> support(aut->num_states());
    if (use_stutter && aut->prop_stutter_invariant())
      {
        // FIXME this could be improved
        // supports of states should account for possible stuttering if we plan
        // to use stuttering invariance
        for (unsigned c = 0; c != scc.scc_count(); ++c)
          {
            bdd c_supp = scc.scc_ap_support(c);
            for (const auto& su: scc.succ(c))
              c_supp &= support[scc.one_state_of(su)];
            for (unsigned st: scc.states_of(c))
              support[st] = c_supp;
          }
      }
    else
      {
        for (unsigned i = 0; i != aut->num_states(); ++i)
          {
            bdd res = bddtrue;
            for (const auto& e : aut->out(i))
              res &= bdd_support(e.cond);
            support[i] = res;
          }
      }

    safra_support safra2letters(support);

    auto res = make_twa_graph(aut->get_dict());
    res->copy_ap_of(aut);
    res->prop_copy(aut,
                   { false, // state based
                       false, // inherently_weak
                       false, false, // deterministic
                       true, // complete
                       true // stutter inv
                       });

    // Given a safra_state get its associated state in output automata.
    // Required to create new edges from 2 safra-state
    power_set seen;
    // As per the standard, references to elements in a std::unordered_set or
    // std::unordered_map are invalidated by erasure only.
    std::deque<std::reference_wrapper<power_set::value_type>> todo;
    auto get_state = [&res, &seen, &todo](const safra_state& s) -> unsigned
      {
        auto i = seen.emplace(std::make_pair(s, 0));
        unsigned dst_num;
        if (i.second) // insertion did take place
          {
            dst_num = res->new_state();
            i.first->second = dst_num;
            todo.emplace_back(*i.first);
          }
        else // element was already in seen
          dst_num = i.first->second;

        return dst_num;
      };

    {
      unsigned init_state = aut->get_init_state_number();
      bool start_accepting =
        !use_scc || scc.is_accepting_scc(scc.scc_of(init_state));
      safra_state init(init_state, start_accepting);
      unsigned num = get_state(init); // inserts both in seen and in todo
      res->set_init_state(num);
    }
    unsigned sets = 0;
    while (!todo.empty())
      {
        const safra_state& curr = todo.front().get().first;
        unsigned src_num = todo.front().get().second;
        todo.pop_front();
        compute_succs succs(curr, aut, seen, scc, implications, is_connected,
                            safra2letters.get(curr), use_scc, use_simulation,
                            use_stutter);
        for (auto s = succs.begin(); s != succs.end(); ++s)
          {
            // Don't construct sink state as complete does a better job at this
            if (s->nodes_.empty())
              continue;
            unsigned dst_num = get_state(*s);
            if (s->color_ != -1U)
              {
                res->new_edge(src_num, dst_num, s.cond(), {s->color_});
                // We only care about green acc which are odd
                if (s->color_ % 2 == 1)
                  sets = std::max(s->color_ + 1, sets);
              }
            else
              res->new_edge(src_num, dst_num, s.cond());
          }
      }
    remove_dead_acc(res, sets);
    // Acceptance is now min(odd) since we can emit Red on paths 0 with new opti
    res->set_acceptance(sets, acc_cond::acc_code::parity(false, true, sets));
    res->prop_universal(true);
    res->prop_state_acc(false);

    if (pretty_print)
      res->set_named_prop("state-names", print_debug(aut, seen));
    return res;
  }
}