acc.hh

// -*- coding: utf-8 -*-
// Copyright (C) 2014-2018 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/>.

#pragma once

#include <functional>
#include <sstream>
#include <vector>
#include <iostream>

#include <spot/misc/_config.h>
#include <spot/misc/bitset.hh>
#include <spot/misc/trival.hh>

namespace spot
{
  namespace internal
  {
    class mark_container;

    template<bool>
    struct _32acc {};
    template<>
    struct _32acc<true>
    {
      SPOT_DEPRECATED("mark_t no longer relies on unsigned, stop using value_t")
      typedef unsigned value_t;
    };
  }

  /// \ingroup twa_essentials
  /// @{

  /// \brief An acceptance condition
  ///
  /// This represent an acceptance condition in the HOA sense, that
  /// is, an acceptance formula plus a number of acceptance sets.  The
  /// acceptance formula is expected to use a subset of the acceptance
  /// sets.  (It usually uses *all* sets, otherwise that means that
  /// some of the sets have no influence on the automaton language and
  /// could be removed.)
  class SPOT_API acc_cond
  {

#ifndef SWIG
  private:
    [[noreturn]] static void report_too_many_sets();
#endif
  public:

    /// \brief An acceptance mark
    ///
    /// This type is used to represent a set of acceptance sets.  It
    /// works (and is implemented) like a bit vector where bit at
    /// index i represents the membership to the i-th acceptance set.
    ///
    /// Typically, each transition of an automaton is labeled by a
    /// mark_t that represents the membership of the transition to
    /// each of the acceptance sets.
    ///
    /// For efficiency reason, the maximum number of acceptance sets
    /// (i.e., the size of the bit vector) supported is a compile-time
    /// constant.  It can be changed by passing an option to the
    /// configure script of Spot.
    struct mark_t :
      public internal::_32acc<SPOT_MAX_ACCSETS == 8*sizeof(unsigned)>
    {
    private:
      // configure guarantees that SPOT_MAX_ACCSETS % (8*sizeof(unsigned)) == 0
      typedef bitset<SPOT_MAX_ACCSETS / (8*sizeof(unsigned))> _value_t;
      _value_t id;

      mark_t(_value_t id) noexcept
        : id(id)
      {
      }

    public:
      /// Initialize an empty mark_t.
      mark_t() = default;

#ifndef SWIG
      /// Create a mark_t from a range of set numbers.
      template<class iterator>
      mark_t(const iterator& begin, const iterator& end)
        : mark_t(_value_t::zero())
      {
        for (iterator i = begin; i != end; ++i)
          set(*i);
      }

      /// Create a mark_t from a list of set numbers.
      mark_t(std::initializer_list<unsigned> vals)
        : mark_t(vals.begin(), vals.end())
      {
      }

      SPOT_DEPRECATED("use brace initialization instead")
      mark_t(unsigned i)
      {
        unsigned j = 0;
        while (i)
          {
            if (i & 1U)
              this->set(j);
            ++j;
            i >>= 1;
          }
      }
#endif

      /// \brief The maximum number of acceptance sets supported by
      /// this implementation.
      ///
      /// The value can be changed at compile-time using configure's
      /// --enable-max-accsets=N option.
      constexpr static unsigned max_accsets()
      {
        return SPOT_MAX_ACCSETS;
      }

      /// \brief A mark_t with all bits set to one.
      ///
      /// Beware that *all* bits are sets, not just the bits used in
      /// the acceptance condition.  This class is unaware of the
      /// acceptance condition.
      static mark_t all()
      {
        return mark_t(_value_t::mone());
      }

      size_t hash() const noexcept
      {
        std::hash<decltype(id)> h;
        return h(id);
      }

      SPOT_DEPRECATED("compare mark_t to mark_t, not to unsigned")
      bool operator==(unsigned o) const
      {
        SPOT_ASSERT(o == 0U);
        (void)o;
        return !id;
      }

      SPOT_DEPRECATED("compare mark_t to mark_t, not to unsigned")
      bool operator!=(unsigned o) const
      {
        SPOT_ASSERT(o == 0U);
        (void)o;
        return !!id;
      }

      bool operator==(mark_t o) const
      {
        return id == o.id;
      }

      bool operator!=(mark_t o) const
      {
        return id != o.id;
      }

      bool operator<(mark_t o) const
      {
        return id < o.id;
      }

      bool operator<=(mark_t o) const
      {
        return id <= o.id;
      }

      bool operator>(mark_t o) const
      {
        return id > o.id;
      }

      bool operator>=(mark_t o) const
      {
        return id >= o.id;
      }

      explicit operator bool() const
      {
        return !!id;
      }

      bool has(unsigned u) const
      {
        return !!this->operator&(mark_t({0}) << u);
      }

      void set(unsigned u)
      {
        id.set(u);
      }

      void clear(unsigned u)
      {
        id.clear(u);
      }

      mark_t& operator&=(mark_t r)
      {
        id &= r.id;
        return *this;
      }

      mark_t& operator|=(mark_t r)
      {
        id |= r.id;
        return *this;
      }

      mark_t& operator-=(mark_t r)
      {
        id &= ~r.id;
        return *this;
      }

      mark_t& operator^=(mark_t r)
      {
        id ^= r.id;
        return *this;
      }

      mark_t operator&(mark_t r) const
      {
        return id & r.id;
      }

      mark_t operator|(mark_t r) const
      {
        return id | r.id;
      }

      mark_t operator-(mark_t r) const
      {
        return id & ~r.id;
      }

      mark_t operator~() const
      {
        return ~id;
      }

      mark_t operator^(mark_t r) const
      {
        return id ^ r.id;
      }

#if SPOT_DEBUG || defined(SWIGPYTHON)
#  define SPOT_WRAP_OP(ins)                     \
        try                                     \
          {                                     \
            ins;                                \
          }                                     \
        catch (const std::runtime_error& e)     \
          {                                     \
            report_too_many_sets();             \
          }
#else
#  define SPOT_WRAP_OP(ins) ins;
#endif
      mark_t operator<<(unsigned i) const
      {
        SPOT_WRAP_OP(return id << i);
      }

      mark_t& operator<<=(unsigned i)
      {
        SPOT_WRAP_OP(id <<= i; return *this);
      }

      mark_t operator>>(unsigned i) const
      {
        SPOT_WRAP_OP(return id >> i);
      }

      mark_t& operator>>=(unsigned i)
      {
        SPOT_WRAP_OP(id >>= i; return *this);
      }
#undef SPOT_WRAP_OP

      mark_t strip(mark_t y) const
      {
        // strip every bit of id that is marked in y
        //       100101110100.strip(
        //       001011001000)
        //   ==  10 1  11 100
        //   ==      10111100

        auto xv = id;                // 100101110100
        auto yv = y.id;                // 001011001000

        while (yv && xv)
          {
            // Mask for everything after the last 1 in y
            auto rm = (~yv) & (yv - 1);        // 000000000111
            // Mask for everything before the last 1 in y
            auto lm = ~(yv ^ (yv - 1));        // 111111110000
            xv = ((xv & lm) >> 1) | (xv & rm);
            yv = (yv & lm) >> 1;
          }
        return xv;
      }

      /// \brief Whether the set of bits represented by *this is a
      /// subset of those represented by \a m.
      bool subset(mark_t m) const
      {
        return !((*this) - m);
      }

      /// \brief Whether the set of bits represented by *this is a
      /// proper subset of those represented by \a m.
      bool proper_subset(mark_t m) const
      {
        return *this != m && this->subset(m);
      }

      /// \brief Number of bits sets.
      unsigned count() const
      {
        return id.count();
      }

      /// \brief The number of the highest set used plus one.
      ///
      /// If no set is used, this returns 0,
      /// If the sets {1,3,8} are used, this returns 9.
      unsigned max_set() const
      {
        if (id)
          return id.highest()+1;
        else
          return 0;
      }

      /// \brief The number of the lowest set used plus one.
      ///
      /// If no set is used, this returns 0.
      /// If the sets {1,3,8} are used, this returns 2.
      unsigned min_set() const
      {
        if (id)
          return id.lowest()+1;
        else
          return 0;
      }

      /// \brief A mark_t where all bits have been removed except the
      /// lowest one.
      ///
      /// For instance if this contains {1,3,8}, the output is {1}.
      mark_t lowest() const
      {
        return id & -id;
      }

      /// \brief Remove n bits that where set.
      ///
      /// If there are less than n bits set, the output is empty.
      mark_t& remove_some(unsigned n)
      {
        while (n--)
          id &= id - 1;
        return *this;
      }

      /// \brief Fill a container with the indices of the bits that are set.
      template<class iterator>
      void fill(iterator here) const
      {
        auto a = *this;
        unsigned level = 0;
        while (a)
          {
            if (a.has(0))
              *here++ = level;
            ++level;
            a >>= 1;
          }
      }

      /// Returns some iterable object that contains the used sets.
      spot::internal::mark_container sets() const;

      SPOT_API
      friend std::ostream& operator<<(std::ostream& os, mark_t m);
    };

    /// \brief Operators for acceptance formulas.
    enum class acc_op : unsigned short
    { Inf, Fin, InfNeg, FinNeg, And, Or };

    /// \brief A "node" in an acceptance formulas.
    ///
    /// Acceptance formulas are stored as a vector of acc_word in a
    /// kind of reverse polish notation.  Each acc_word is either an
    /// operator, or a set of acceptance sets.  Operators come with a
    /// size that represent the number of words in the subtree,
    /// current operator excluded.
    union acc_word
    {
      mark_t mark;
      struct {
        acc_op op;             // Operator
        unsigned short size; // Size of the subtree (number of acc_word),
                             // not counting this node.
      } sub;
    };

    /// \brief An acceptance formula.
    ///
    /// Acceptance formulas are stored as a vector of acc_word in a
    /// kind of reverse polish notation.  The motivation for this
    /// design was that we could evaluate the acceptance condition
    /// using a very simple stack-based interpreter; however it turned
    /// out that such a stack-based interpretation would prevent us
    /// from doing short-circuit evaluation, so we are not evaluating
    /// acceptance conditions this way, and maybe the implementation
    /// of acc_code could change in the future.  It's best not to rely
    /// on the fact that formulas are stored as vectors.  Use the
    /// provided methods instead.
    struct SPOT_API acc_code: public std::vector<acc_word>
    {
      bool operator==(const acc_code& other) const
      {
        unsigned pos = size();
        if (other.size() != pos)
          return false;
        while (pos > 0)
          {
            auto op = (*this)[pos - 1].sub.op;
            auto sz = (*this)[pos - 1].sub.size;
            if (other[pos - 1].sub.op != op ||
                other[pos - 1].sub.size != sz)
              return false;
            switch (op)
              {
              case acc_cond::acc_op::And:
              case acc_cond::acc_op::Or:
                --pos;
                break;
              case acc_cond::acc_op::Inf:
              case acc_cond::acc_op::InfNeg:
              case acc_cond::acc_op::Fin:
              case acc_cond::acc_op::FinNeg:
                pos -= 2;
                if (other[pos].mark != (*this)[pos].mark)
                  return false;
                break;
              }
          }
        return true;
      };

      bool operator<(const acc_code& other) const
      {
        unsigned pos = size();
        auto osize = other.size();
        if (pos < osize)
          return true;
        if (pos > osize)
          return false;
        while (pos > 0)
          {
            auto op = (*this)[pos - 1].sub.op;
            auto oop = other[pos - 1].sub.op;
            if (op < oop)
              return true;
            if (op > oop)
              return false;
            auto sz = (*this)[pos - 1].sub.size;
            auto osz = other[pos - 1].sub.size;
            if (sz < osz)
              return true;
            if (sz > osz)
              return false;
            switch (op)
              {
              case acc_cond::acc_op::And:
              case acc_cond::acc_op::Or:
                --pos;
                break;
              case acc_cond::acc_op::Inf:
              case acc_cond::acc_op::InfNeg:
              case acc_cond::acc_op::Fin:
              case acc_cond::acc_op::FinNeg:
                {
                  pos -= 2;
                  auto m = (*this)[pos].mark;
                  auto om = other[pos].mark;
                  if (m < om)
                    return true;
                  if (m > om)
                    return false;
                  break;
                }
              }
          }
        return false;
      }

      bool operator>(const acc_code& other) const
      {
        return other < *this;
      }

      bool operator<=(const acc_code& other) const
      {
        return !(other < *this);
      }

      bool operator>=(const acc_code& other) const
      {
        return !(*this < other);
      }

      bool operator!=(const acc_code& other) const
      {
        return !(*this == other);
      }

      /// \brief Is this the "true" acceptance condition?
      ///
      /// This corresponds to "t" in the HOA format.  Under this
      /// acceptance condition, all runs are accepting.
      bool is_t() const
      {
        // We store "t" as an empty condition, or as Inf({}).
        unsigned s = size();
        return s == 0 || ((*this)[s - 1].sub.op == acc_op::Inf
                          && !((*this)[s - 2].mark));
      }

      /// \brief Is this the "false" acceptance condition?
      ///
      /// This corresponds to "f" in the HOA format.  Under this
      /// acceptance condition, no runs is accepting.  Obviously, this
      /// has very few practical application, except as neutral
      /// element in some construction.
      bool is_f() const
      {
        // We store "f" as Fin({}).
        unsigned s = size();
        return s > 1
          && (*this)[s - 1].sub.op == acc_op::Fin && !((*this)[s - 2].mark);
      }

      /// \brief Construct the "false" acceptance condition.
      ///
      /// This corresponds to "f" in the HOA format.  Under this
      /// acceptance condition, no runs is accepting.  Obviously, this
      /// has very few practical application, except as neutral
      /// element in some construction.
      static acc_code f()
      {
        acc_code res;
        res.resize(2);
        res[0].mark = {};
        res[1].sub.op = acc_op::Fin;
        res[1].sub.size = 1;
        return res;
      }

      /// \brief Construct the "true" acceptance condition.
      ///
      /// This corresponds to "t" in the HOA format.  Under this
      /// acceptance condition, all runs are accepting.
      static acc_code t()
      {
        return {};
      }

      /// \brief Construct a generalized co-Büchi acceptance
      ///
      /// For the input m={1,8,9}, this constructs Fin(1)|Fin(8)|Fin(9).
      ///
      /// Internally, such a formula is stored using a single word
      /// Fin({1,8,9}).
      /// @{
      static acc_code fin(mark_t m)
      {
        acc_code res;
        res.resize(2);
        res[0].mark = m;
        res[1].sub.op = acc_op::Fin;
        res[1].sub.size = 1;
        return res;
      }

      static acc_code fin(std::initializer_list<unsigned> vals)
      {
        return fin(mark_t(vals));
      }
      /// @}

      /// \brief Construct a generalized co-Büchi acceptance for
      /// complemented sets.
      ///
      /// For the input `m={1,8,9}`, this constructs
      /// `Fin(!1)|Fin(!8)|Fin(!9)`.
      ///
      /// Internally, such a formula is stored using a single word
      /// `FinNeg({1,8,9})`.
      ///
      /// Note that `FinNeg` formulas are not supported by most methods
      /// of this class, and not supported by algorithms in Spot.
      /// This is mostly used in the parser for HOA files: if the
      /// input file uses `Fin(!0)` as acceptance condition, the
      /// condition will eventually be rewritten as `Fin(0)` by toggling
      /// the membership to set 0 of each transition.
      /// @{
      static acc_code fin_neg(mark_t m)
      {
        acc_code res;
        res.resize(2);
        res[0].mark = m;
        res[1].sub.op = acc_op::FinNeg;
        res[1].sub.size = 1;
        return res;
      }

      static acc_code fin_neg(std::initializer_list<unsigned> vals)
      {
        return fin_neg(mark_t(vals));
      }
      /// @}

      /// \brief Construct a generalized Büchi acceptance
      ///
      /// For the input `m={1,8,9}`, this constructs
      /// `Inf(1)&Inf(8)&Inf(9)`.
      ///
      /// Internally, such a formula is stored using a single word
      /// `Inf({1,8,9})`.
      /// @{
      static acc_code inf(mark_t m)
      {
        acc_code res;
        res.resize(2);
        res[0].mark = m;
        res[1].sub.op = acc_op::Inf;
        res[1].sub.size = 1;
        return res;
      }

      static acc_code inf(std::initializer_list<unsigned> vals)
      {
        return inf(mark_t(vals));
      }
      /// @}

      /// \brief Construct a generalized Büchi acceptance for
      /// complemented sets.
      ///
      /// For the input `m={1,8,9}`, this constructs
      /// `Inf(!1)&Inf(!8)&Inf(!9)`.
      ///
      /// Internally, such a formula is stored using a single word
      /// `InfNeg({1,8,9})`.
      ///
      /// Note that `InfNeg` formulas are not supported by most methods
      /// of this class, and not supported by algorithms in Spot.
      /// This is mostly used in the parser for HOA files: if the
      /// input file uses `Inf(!0)` as acceptance condition, the
      /// condition will eventually be rewritten as `Inf(0)` by toggling
      /// the membership to set 0 of each transition.
      /// @{
      static acc_code inf_neg(mark_t m)
      {
        acc_code res;
        res.resize(2);
        res[0].mark = m;
        res[1].sub.op = acc_op::InfNeg;
        res[1].sub.size = 1;
        return res;
      }

      static acc_code inf_neg(std::initializer_list<unsigned> vals)
      {
        return inf_neg(mark_t(vals));
      }
      /// @}

      /// \brief Build a Büchi acceptance condition.
      ///
      /// This builds the formula `Inf(0)`.
      static acc_code buchi()
      {
        return inf({0});
      }

      /// \brief Build a co-Büchi acceptance condition.
      ///
      /// This builds the formula `Fin(0)`.
      static acc_code cobuchi()
      {
        return fin({0});
      }

      /// \brief Build a generalized-Büchi acceptance condition with n sets
      ///
      /// This builds the formula `Inf(0)&Inf(1)&...&Inf(n-1)`.
      ///
      /// When n is zero, the acceptance condition reduces to true.
      static acc_code generalized_buchi(unsigned n)
      {
        if (n == 0)
          return inf({});
        acc_cond::mark_t m = mark_t::all();
        m >>= mark_t::max_accsets() - n;
        return inf(m);
      }

      /// \brief Build a generalized-co-Büchi acceptance condition with n sets
      ///
      /// This builds the formula `Fin(0)|Fin(1)|...|Fin(n-1)`.
      ///
      /// When n is zero, the acceptance condition reduces to false.
      static acc_code generalized_co_buchi(unsigned n)
      {
        if (n == 0)
          return fin({});
        acc_cond::mark_t m = mark_t::all();
        m >>= mark_t::max_accsets() - n;
        return fin(m);
      }

      /// \brief Build a Rabin condition with n pairs.
      ///
      /// This builds the formula
      /// `(Fin(0)&Inf(1))|(Fin(2)&Inf(3))|...|(Fin(2n-2)&Inf(2n-1))`
      static acc_code rabin(unsigned n)
      {
        acc_cond::acc_code res = f();
        while (n > 0)
          {
            res |= inf({2*n - 1}) & fin({2*n - 2});
            --n;
          }
        return res;
      }

      /// \brief Build a Streett condition with n pairs.
      ///
      /// This builds the formula
      /// `(Fin(0)|Inf(1))&(Fin(2)|Inf(3))&...&(Fin(2n-2)|Inf(2n-1))`
      static acc_code streett(unsigned n)
      {
        acc_cond::acc_code res = t();
        while (n > 0)
          {
            res &= inf({2*n - 1}) | fin({2*n - 2});
            --n;
          }
        return res;
      }

      /// \brief Build a generalized Rabin condition.
      ///
      /// The two iterators should point to a range of integers, each
      /// integer being the number of Inf term in a generalized Rabin pair.
      ///
      /// For instance if the input is `[2,3,0]`, the output
      /// will have three clauses (=generalized pairs), with 2 Inf terms in
      /// the first clause, 3 in the second, and 0 in the last:
      ///   `(Fin(0)&Inf(1)&Inf(2))|Fin(3)&Inf(4)&Inf(5)&Inf(6)|Fin(7)`.
      ///
      /// Since set numbers are not reused, the number of sets used is
      /// the sum of all input integers plus their count.
      template<class Iterator>
      static acc_code generalized_rabin(Iterator begin, Iterator end)
      {
        acc_cond::acc_code res = f();
        unsigned n = 0;
        for (Iterator i = begin; i != end; ++i)
          {
            unsigned f = n++;
            acc_cond::mark_t m = {};
            for (unsigned ni = *i; ni > 0; --ni)
              m.set(n++);
            auto pair = inf(m) & fin({f});
            std::swap(pair, res);
            res |= std::move(pair);
          }
        return res;
      }

      /// \brief Build a parity acceptance condition
      ///
      /// In parity acceptance a word is accepting if the maximum (or
      /// minimum) set number that is seen infinitely often is odd (or
      /// even).  This function will build a formula for that, as
      /// specified in the HOA format.
      static acc_code parity(bool max, bool odd, unsigned sets);

      /// \brief Build a random acceptance condition
      ///
      /// If \a n is 0, this will always generate the true acceptance,
      /// because working with false acceptance is somehow pointless.
      ///
      /// For \a n>0, we randomly create a term Fin(i) or Inf(i) for
      /// each set 0≤i<n.  If \a reuse>0.0, it gives the probability
      /// that a set i can generate more than one Fin(i)/Inf(i) term.
      /// Set i will be reused as long as our [0,1) random number
      /// generator gives a value ≤reuse.  (Do not set reuse≥1.0 as
      /// that will give an infinite loop.)
      ///
      /// All these Fin/Inf terms are the leaves of the tree we are
      /// building.  That tree is then build by picking two random
      /// subtrees, and joining them with & and | randomly, until we
      /// are left with a single tree.
      static acc_code random(unsigned n, double reuse = 0.0);

      /// \brief Conjunct the current condition in place with \a r.
      acc_code& operator&=(const acc_code& r)
      {
        if (is_t() || r.is_f())
          {
            *this = r;
            return *this;
          }
        if (is_f() || r.is_t())
          return *this;
        unsigned s = size() - 1;
        unsigned rs = r.size() - 1;
        // We want to group all Inf(x) operators:
        //   Inf(a) & Inf(b) = Inf(a & b)
        if (((*this)[s].sub.op == acc_op::Inf
             && r[rs].sub.op == acc_op::Inf)
            || ((*this)[s].sub.op == acc_op::InfNeg
                && r[rs].sub.op == acc_op::InfNeg))
          {
            (*this)[s - 1].mark |= r[rs - 1].mark;
            return *this;
          }

        // In the more complex scenarios, left and right may both
        // be conjunctions, and Inf(x) might be a member of each
        // side.  Find it if it exists.
        // left_inf points to the left Inf mark if any.
        // right_inf points to the right Inf mark if any.
        acc_word* left_inf = nullptr;
        if ((*this)[s].sub.op == acc_op::And)
          {
            auto start = &(*this)[s] - (*this)[s].sub.size;
            auto pos = &(*this)[s] - 1;
            pop_back();
            while (pos > start)
              {
                if (pos->sub.op == acc_op::Inf)
                  {
                    left_inf = pos - 1;
                    break;
                  }
                pos -= pos->sub.size + 1;
              }
          }
        else if ((*this)[s].sub.op == acc_op::Inf)
          {
            left_inf = &(*this)[s - 1];
          }

        const acc_word* right_inf = nullptr;
        auto right_end = &r.back();
        if (right_end->sub.op == acc_op::And)
          {
            auto start = &r[0];
            auto pos = --right_end;
            while (pos > start)
            {
              if (pos->sub.op == acc_op::Inf)
                {
                  right_inf = pos - 1;
                  break;
                }
              pos -= pos->sub.size + 1;
            }
          }
        else if (right_end->sub.op == acc_op::Inf)
          {
            right_inf = right_end - 1;
          }

        acc_cond::mark_t carry = {};
        if (left_inf && right_inf)
          {
            carry = left_inf->mark;
            auto pos = left_inf - &(*this)[0];
            erase(begin() + pos, begin() + pos + 2);
          }
        auto sz = size();
        insert(end(), &r[0], right_end + 1);
        if (carry)
          (*this)[sz + (right_inf - &r[0])].mark |= carry;

        acc_word w;
        w.sub.op = acc_op::And;
        w.sub.size = size();
        emplace_back(w);
        return *this;
      }

      /// \brief Conjunct the current condition with \a r.
      acc_code operator&(const acc_code& r) const
      {
        acc_code res = *this;
        res &= r;
        return res;
      }

      /// \brief Conjunct the current condition with \a r.
      acc_code operator&(acc_code&& r) const
      {
        acc_code res = *this;
        res &= r;
        return res;
      }

      /// \brief Disjunct the current condition in place with \a r.
      acc_code& operator|=(const acc_code& r)
      {
        if (is_t() || r.is_f())
          return *this;
        if (is_f() || r.is_t())
          {
            *this = r;
            return *this;
          }
        unsigned s = size() - 1;
        unsigned rs = r.size() - 1;
        // Fin(a) | Fin(b) = Fin(a | b)
        if (((*this)[s].sub.op == acc_op::Fin
             && r[rs].sub.op == acc_op::Fin)
            || ((*this)[s].sub.op == acc_op::FinNeg
                && r[rs].sub.op == acc_op::FinNeg))
          {
            (*this)[s - 1].mark |= r[rs - 1].mark;
            return *this;
          }

        // In the more complex scenarios, left and right may both
        // be disjunctions, and Fin(x) might be a member of each
        // side.  Find it if it exists.
        // left_inf points to the left Inf mark if any.
        // right_inf points to the right Inf mark if any.
        acc_word* left_fin = nullptr;
        if ((*this)[s].sub.op == acc_op::Or)
          {
            auto start = &(*this)[s] - (*this)[s].sub.size;
            auto pos = &(*this)[s] - 1;
            pop_back();
            while (pos > start)
              {
                if (pos->sub.op == acc_op::Fin)
                  {
                    left_fin = pos - 1;
                    break;
                  }
                pos -= pos->sub.size + 1;
              }
          }
        else if ((*this)[s].sub.op == acc_op::Fin)
          {
            left_fin = &(*this)[s - 1];
          }

        const acc_word* right_fin = nullptr;
        auto right_end = &r.back();
        if (right_end->sub.op == acc_op::Or)
          {
            auto start = &r[0];
            auto pos = --right_end;
            while (pos > start)
            {
              if (pos->sub.op == acc_op::Fin)
                {
                  right_fin = pos - 1;
                  break;
                }
              pos -= pos->sub.size + 1;
            }
          }
        else if (right_end->sub.op == acc_op::Fin)
          {
            right_fin = right_end - 1;
          }

        acc_cond::mark_t carry = {};
        if (left_fin && right_fin)
          {
            carry = left_fin->mark;
            auto pos = (left_fin - &(*this)[0]);
            this->erase(begin() + pos, begin() + pos + 2);
          }
        auto sz = size();
        insert(end(), &r[0], right_end + 1);
        if (carry)
          (*this)[sz + (right_fin - &r[0])].mark |= carry;
        acc_word w;
        w.sub.op = acc_op::Or;
        w.sub.size = size();
        emplace_back(w);
        return *this;
      }

      /// \brief Disjunct the current condition with \a r.
      acc_code operator|(acc_code&& r) const
      {
        acc_code res = *this;
        res |= r;
        return res;
      }

      /// \brief Disjunct the current condition with \a r.
      acc_code operator|(const acc_code& r) const
      {
        acc_code res = *this;
        res |= r;
        return res;
      }

      /// \brief Apply a left shift to all mark_t that appear in the condition.
      ///
      /// Shifting `Fin(0)&Inf(3)` by 2 will give `Fin(2)&Inf(5)`.
      ///
      /// The result is modified in place.
      acc_code& operator<<=(unsigned sets)
      {
        if (SPOT_UNLIKELY(sets >= mark_t::max_accsets()))
          report_too_many_sets();
        if (empty())
          return *this;
        unsigned pos = size();
        do
          {
            switch ((*this)[pos - 1].sub.op)
              {
              case acc_cond::acc_op::And:
              case acc_cond::acc_op::Or:
                --pos;
                break;
              case acc_cond::acc_op::Inf:
              case acc_cond::acc_op::InfNeg:
              case acc_cond::acc_op::Fin:
              case acc_cond::acc_op::FinNeg:
                pos -= 2;
                (*this)[pos].mark <<= sets;
                break;
              }
          }
        while (pos > 0);
        return *this;
      }