acc.hh 25.5 KB
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// -*- coding: utf-8 -*-
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// Copyright (C) 2014, 2015 Laboratoire de Recherche et Développement de
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// 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/>.

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#pragma once
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#include <functional>
#include <unordered_map>
#include <sstream>
#include <vector>
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#include <spot/tl/defaultenv.hh>
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#include <iostream>
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namespace spot
{
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  class SPOT_API acc_cond
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  {
  public:
    struct mark_t
    {
      typedef unsigned value_t;
      value_t id;

      mark_t() = default;

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

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      template<class iterator>
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      mark_t(const iterator& begin, const iterator& end) noexcept
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      {
	id = 0U;
	for (iterator i = begin; i != end; ++i)
	  set(*i);
      }

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      mark_t(std::initializer_list<unsigned> vals) noexcept
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	: mark_t(vals.begin(), vals.end())
      {
      }

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      bool operator==(unsigned o) const
      {
	assert(o == 0U);
	return id == o;
      }

      bool operator!=(unsigned o) const
      {
	assert(o == 0U);
	return id != o;
      }

      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;
      }

      operator bool() const
      {
	return id != 0;
      }

      bool has(unsigned u) const
      {
	return id & (1U << u);
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      }

      void set(unsigned u)
      {
	id |= (1U << u);
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      }

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      void clear(unsigned u)
      {
	id &= ~(1U << u);
      }

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      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;
      }

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

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      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;
      }

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

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

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

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

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

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

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      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;
      }

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      // Number of bits sets.
      unsigned count() const
      {
#ifdef __GNUC__
	return __builtin_popcount(id);
#else
	unsigned c = 0U;
	auto v = id;
	while (v)
	  {
	    ++c;
	    v &= v - 1;
	  }
	return c;
#endif
      }

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      // Return the number of the highest set used plus one.
      // So if no set is used, this returns 0,
      // but if the sets {1,3,8} are used, this returns 9.
      unsigned max_set() const
      {
	auto i = id;
	int res = 0;
	while (i)
	  {
	    ++res;
	    i >>= 1;
	  }
	return res;
      }

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      // Return the lowest acceptance mark
      mark_t lowest() const
      {
	return id & -id;
      }

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      // Remove n bits that where set
      mark_t& remove_some(unsigned n)
      {
	while (n--)
	  id &= id - 1;
	return *this;
      }

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      template<class iterator>
      void fill(iterator here) const
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      {
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	auto a = id;
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	unsigned level = 0;
	while (a)
	  {
	    if (a & 1)
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	      *here++ = level;
	    ++level;
	    a >>= 1;
	  }
      }

      // FIXME: Return some iterable object without building a vector.
      std::vector<unsigned> sets() const
      {
	std::vector<unsigned> res;
	fill(std::back_inserter(res));
	return res;
      }

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

    // This encodes either an operator or set of acceptance sets.
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    enum class acc_op : unsigned short
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    { Inf, Fin, InfNeg, FinNeg, And, Or };
    union acc_word
    {
      mark_t mark;
      struct {
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	acc_op op;	     // Operator
	unsigned short size; // Size of the subtree (number of acc_word),
			     // not counting this node.
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      };
    };

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    struct SPOT_API acc_code: public std::vector<acc_word>
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    {
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      bool operator==(const acc_code& other) const
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      {
	unsigned pos = size();
	if (other.size() != pos)
	  return false;
	while (pos > 0)
	  {
	    auto op = (*this)[pos - 1].op;
	    auto sz = (*this)[pos - 1].size;
	    if (other[pos - 1].op != op ||
		other[pos - 1].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;
      };

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      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].op;
	    auto oop = other[pos - 1].op;
	    if (op < oop)
	      return true;
	    if (op > oop)
	      return false;
	    auto sz = (*this)[pos - 1].size;
	    auto osz = other[pos - 1].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
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      {
	return !(*this == other);
      }

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      bool is_t() const
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      {
	unsigned s = size();
	return s == 0
	  || ((*this)[s - 1].op == acc_op::Inf && (*this)[s - 2].mark == 0U);
      }

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      bool is_f() const
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      {
	unsigned s = size();
	return s > 1
	  && (*this)[s - 1].op == acc_op::Fin && (*this)[s - 2].mark == 0U;
      }

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      static acc_code f()
      {
	acc_code res;
	res.resize(2);
	res[0].mark = 0U;
	res[1].op = acc_op::Fin;
	res[1].size = 1;
	return res;
      }

      static acc_code t()
      {
	return {};
      }

      static acc_code fin(mark_t m)
      {
	acc_code res;
	res.resize(2);
	res[0].mark = m;
	res[1].op = acc_op::Fin;
	res[1].size = 1;
	return res;
      }

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

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      static acc_code fin_neg(mark_t m)
      {
	acc_code res;
	res.resize(2);
	res[0].mark = m;
	res[1].op = acc_op::FinNeg;
	res[1].size = 1;
	return res;
      }

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

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      static acc_code inf(mark_t m)
      {
	acc_code res;
	res.resize(2);
	res[0].mark = m;
	res[1].op = acc_op::Inf;
	res[1].size = 1;
	return res;
      }

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

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      static acc_code inf_neg(mark_t m)
      {
	acc_code res;
	res.resize(2);
	res[0].mark = m;
	res[1].op = acc_op::InfNeg;
	res[1].size = 1;
	return res;
      }

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

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      static acc_code buchi()
      {
	return inf({0});
      }

      static acc_code cobuchi()
      {
	return fin({0});
      }

      static acc_code generalized_buchi(unsigned n)
      {
	acc_cond::mark_t m = (1U << n) - 1;
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	if (n == 8 * sizeof(mark_t::value_t))
	  m = mark_t(-1U);
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	return inf(m);
      }

      static acc_code generalized_co_buchi(unsigned n)
      {
	acc_cond::mark_t m = (1U << n) - 1;
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	if (n == 8 * sizeof(mark_t::value_t))
	  m = mark_t(-1U);
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	return fin(m);
      }

      // n is a number of pairs.
      static acc_code rabin(unsigned n)
      {
	acc_cond::acc_code res = f();
	while (n > 0)
	  {
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	    res |= inf({2*n - 1}) & fin({2*n - 2});
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	    --n;
	  }
	return res;
      }

       // n is a number of pairs.
      static acc_code streett(unsigned n)
      {
	acc_cond::acc_code res = t();
	while (n > 0)
	  {
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	    res &= inf({2*n - 1}) | fin({2*n - 2});
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	    --n;
	  }
	return res;
      }

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      template<class Iterator>
      static acc_code generalized_rabin(Iterator begin, Iterator end)
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      {
	acc_cond::acc_code res = f();
	unsigned n = 0;
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	for (Iterator i = begin; i != end; ++i)
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	  {
	    acc_cond::acc_code pair = fin({n++});
	    acc_cond::mark_t m = 0U;
	    for (unsigned ni = *i; ni > 0; --ni)
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	      m.set(n++);
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	    pair &= inf(m);
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	    std::swap(pair, res);
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	    res |= std::move(pair);
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	  }
	return res;
      }

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      static acc_code parity(bool max, bool odd, unsigned sets);

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      // Number of acceptance sets to use, and probability to reuse
      // each set another time after it has been used in the
      // acceptance formula.
      static acc_code random(unsigned n, double reuse = 0.0);

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      acc_code& operator&=(acc_code&& r)
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      {
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	if (is_t() || r.is_f())
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	  {
	    *this = std::move(r);
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	    return *this;
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	  }
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	if (is_f() || r.is_t())
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	  return *this;
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	unsigned s = size() - 1;
	unsigned rs = r.size() - 1;
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	// We want to group all Inf(x) operators:
	//   Inf(a) & Inf(b) = Inf(a & b)
	if (((*this)[s].op == acc_op::Inf && r[rs].op == acc_op::Inf)
	    || ((*this)[s].op == acc_op::InfNeg && r[rs].op == acc_op::InfNeg))
	  {
	    (*this)[s - 1].mark |= r[rs - 1].mark;
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	    return *this;
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	  }

	// 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].op == acc_op::And)
	  {
	    auto start = &(*this)[s] - (*this)[s].size;
	    auto pos = &(*this)[s] - 1;
	    pop_back();
	    while (pos > start)
	      {
		if (pos->op == acc_op::Inf)
		  {
		    left_inf = pos - 1;
		    break;
		  }
		pos -= pos->size + 1;
	      }
	  }
	else if ((*this)[s].op == acc_op::Inf)
	  {
	    left_inf = &(*this)[s - 1];
	  }

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

	if (left_inf && right_inf)
	  {
	    left_inf->mark |= right_inf->mark;
	    insert(this->end(), &r[0], right_inf);
	    insert(this->end(), right_inf + 2, right_end + 1);
	  }
	else if (right_inf)
	  {
	    // Always insert Inf() at the very first entry.
	    insert(this->begin(), right_inf, right_inf + 2);
	    insert(this->end(), &r[0], right_inf);
	    insert(this->end(), right_inf + 2, right_end + 1);
	  }
	else
	  {
	    insert(this->end(), &r[0], right_end + 1);
	  }

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

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      acc_code& operator&=(const acc_code& r)
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      {
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	if (is_t() || r.is_f())
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	  {
	    *this = r;
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	    return *this;
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	  }
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	if (is_f() || r.is_t())
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	  return *this;
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	unsigned s = size() - 1;
	unsigned rs = r.size() - 1;
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	// Inf(a) & Inf(b) = Inf(a & b)
	if (((*this)[s].op == acc_op::Inf && r[rs].op == acc_op::Inf)
	    || ((*this)[s].op == acc_op::InfNeg && r[rs].op == acc_op::InfNeg))
	  {
	    (*this)[s - 1].mark |= r[rs - 1].mark;
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	    return *this;
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	  }
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	// 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;
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	if ((*this)[s].op == acc_op::And)
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	  {
	    auto start = &(*this)[s] - (*this)[s].size;
	    auto pos = &(*this)[s] - 1;
	    pop_back();
	    while (pos > start)
	      {
		if (pos->op == acc_op::Inf)
		  {
		    left_inf = pos - 1;
		    break;
		  }
		pos -= pos->size + 1;
	      }
	  }
	else if ((*this)[s].op == acc_op::Inf)
	  {
	    left_inf = &(*this)[s - 1];
	  }

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

	if (left_inf && right_inf)
	  {
	    left_inf->mark |= right_inf->mark;
	    insert(this->end(), &r[0], right_inf);
	    insert(this->end(), right_inf + 2, right_end + 1);
	  }
	else if (right_inf)
	  {
	    // Always insert Inf() at the very first entry.
	    insert(this->begin(), right_inf, right_inf + 2);
	    insert(this->end(), &r[0], right_inf);
	    insert(this->end(), right_inf + 2, right_end + 1);
	  }
	else
	  {
	    insert(this->end(), &r[0], right_end + 1);
	  }

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

      acc_code operator&(acc_code&& r)
      {
	acc_code res = *this;
	res &= r;
	return res;
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      }

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      acc_code operator&(const acc_code& r)
      {
	acc_code res = *this;
	res &= r;
	return res;
      }

      acc_code& operator|=(acc_code&& r)
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      {
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	if (is_t() || r.is_f())
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	  return *this;
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	if (is_f() || r.is_t())
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	  {
	    *this = std::move(r);
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	    return *this;
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	  }
	unsigned s = size() - 1;
	unsigned rs = r.size() - 1;
	// Fin(a) | Fin(b) = Fin(a | b)
	if (((*this)[s].op == acc_op::Fin && r[rs].op == acc_op::Fin)
	    || ((*this)[s].op == acc_op::FinNeg && r[rs].op == acc_op::FinNeg))
	  {
	    (*this)[s - 1].mark |= r[rs - 1].mark;
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	    return *this;
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	  }
	if ((*this)[s].op == acc_op::Or)
	  pop_back();
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	if (r.back().op == acc_op::Or)
	  r.pop_back();
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	insert(this->end(), r.begin(), r.end());
	acc_word w;
	w.op = acc_op::Or;
	w.size = size();
	push_back(w);
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	return *this;
      }

      acc_code& operator|=(const acc_code& r)
      {
	return *this |= acc_code(r);
      }

      acc_code operator|(acc_code&& r)
      {
	acc_code res = *this;
	res |= r;
	return res;
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      }

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      acc_code operator|(const acc_code& r)
      {
	acc_code res = *this;
	res |= r;
	return res;
      }

      acc_code& operator<<=(unsigned sets)
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      {
	if (empty())
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	  return *this;
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	unsigned pos = size();
	do
	  {
	    switch ((*this)[pos - 1].op)
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	      {
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	      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.id <<= sets;
		break;
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	      }
	  }
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	while (pos > 0);
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	return *this;
      }

      acc_code operator<<(unsigned sets) const
      {
	acc_code res = *this;
	res <<= sets;
	return res;
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      }
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      bool is_dnf() const;
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      bool is_cnf() const;
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      acc_code to_dnf() const;
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      acc_code to_cnf() const;
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      acc_code complement() const;

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      // Return a list of acceptance marks needed to close a cycle
      // that already visit INF infinitely often, so that the cycle is
      // accepting (ACCEPTING=true) or rejecting (ACCEPTING=false).
      // Positive values describe positive set.
      // A negative value x means the set -x-1 must be absent.
      std::vector<std::vector<int>>
	missing(mark_t inf, bool accepting) const;

      bool accepting(mark_t inf) const;

      bool inf_satisfiable(mark_t inf) const;

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      // Remove all the acceptance sets in rem.
      //
      // If MISSING is set, the acceptance sets are assumed to be
      // missing from the automaton, and the acceptance is updated to
      // reflect this.  For instance (Inf(1)&Inf(2))|Fin(3) will
      // become Fin(3) if we remove 2 because it is missing from this
      // automaton, because there is no way to fulfill Inf(1)&Inf(2)
      // in this case.  So essentially MISSING causes Inf(rem) to
      // become f, and Fin(rem) to become t.
      //
      // If MISSING is unset, Inf(rem) become t while Fin(rem) become
      // f.  Removing 2 from (Inf(1)&Inf(2))|Fin(3) would then give
      // Inf(1)|Fin(3).
      acc_code strip(acc_cond::mark_t rem, bool missing) const;

      // Return the set of sets appearing in the condition.
      acc_cond::mark_t used_sets() const;

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      // Return the sets used as Inf or Fin in the acceptance condition
      std::pair<acc_cond::mark_t, acc_cond::mark_t> used_inf_fin_sets() const;

      // Print the acceptance as HTML.  The set_printer function can
      // be used to implement customized output for set numbers.
      std::ostream&
      to_html(std::ostream& os,
	      std::function<void(std::ostream&, int)>
	      set_printer = nullptr) const;

      // Print the acceptance as text.  The set_printer function can
      // be used to implement customized output for set numbers.
      std::ostream&
      to_text(std::ostream& os,
	      std::function<void(std::ostream&, int)>
	      set_printer = nullptr) const;

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      /// \brief Construct an acc_code from a string.
      ///
      /// The string can follow the following grammar:
      ///
      /// <pre>
      ///   acc ::= "t"
      ///         | "f"
      ///         | "Inf" "(" num ")"
      ///         | "Fin" "(" num ")"
      ///         | "(" acc ")"
      ///         | acc "&" acc
      ///         | acc "|" acc
      /// </pre>
      ///
      /// Where num is an integer and "&" has priority over "|".  Note that
      /// "Fin(!x)" and "Inf(!x)" are not supported by this parser.
      ///
      /// Or the string can be the name of an acceptance condition, as
      /// speficied in the HOA format.  (E.g. "Rabin 2", "parity max odd 3",
      /// "generalized-Rabin 4 2 1", etc.).
      ///
      /// A spot::parse_error is thrown on syntax error.
      acc_code(const char* input);

      /// \brief Build an empty acceptance condition.
      ///
      /// This is the same as t().
      acc_code()
      {
      }

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      // Calls to_text
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      SPOT_API
      friend std::ostream& operator<<(std::ostream& os, const acc_code& code);
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    };

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    acc_cond(unsigned n_sets = 0, const acc_code& code = {})
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      : num_(0U), all_(0U), code_(code)
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    {
      add_sets(n_sets);
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      uses_fin_acceptance_ = check_fin_acceptance();
    }

    acc_cond(const acc_code& code)
      : num_(0U), all_(0U), code_(code)
    {
      add_sets(code.used_sets().max_set());
      uses_fin_acceptance_ = check_fin_acceptance();
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    }

    acc_cond(const acc_cond& o)
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      : num_(o.num_), all_(o.all_), code_(o.code_),
        uses_fin_acceptance_(o.uses_fin_acceptance_)
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    {
    }

    ~acc_cond()
    {
    }

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    void set_acceptance(const acc_code& code)
    {
      code_ = code;
      uses_fin_acceptance_ = check_fin_acceptance();
    }

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    const acc_code& get_acceptance() const
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    {
      return code_;
    }

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    acc_code& get_acceptance()
    {
      return code_;
    }

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    bool uses_fin_acceptance() const
    {
      return uses_fin_acceptance_;
    }

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    bool is_t() const
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    {
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      return code_.is_t();
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    }

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    bool is_all() const
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    {
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      return num_ == 0 && is_t();
    }

    bool is_f() const
    {
      return code_.is_f();
    }

    bool is_none() const
    {
      return num_ == 0 && is_f();
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    }

    bool is_buchi() const
    {
      unsigned s = code_.size();
      return num_ == 1 &&
	s == 2 && code_[1].op == acc_op::Inf && code_[0].mark == all_sets();
    }

    bool is_co_buchi() const
    {
      return num_ == 1 && is_generalized_co_buchi();
    }

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    void set_generalized_buchi()
    {
      set_acceptance(inf(all_sets()));
    }

    bool is_generalized_buchi() const
    {
      unsigned s = code_.size();
      return (s == 0 && num_ == 0) ||
	(s == 2 && code_[1].op == acc_op::Inf && code_[0].mark == all_sets());
    }

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    bool is_generalized_co_buchi() const
    {
      unsigned s = code_.size();
      return (s == 2 &&
	      code_[1].op == acc_op::Fin && code_[0].mark == all_sets());
    }

    // Returns a number of pairs (>=0) if Rabin, or -1 else.
    int is_rabin() const;
    // Returns a number of pairs (>=0) if Streett, or -1 else.
    int is_streett() const;

    // Return the number of Inf in each pair.
    bool is_generalized_rabin(std::vector<unsigned>& pairs) const;

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    // If EQUIV is false, this return true iff the acceptance
    // condition is a parity condition written in the canonical way
    // given in the HOA specifications.  If EQUIV is true, then we
    // check whether the condition is logically equivalent to some
    // parity acceptance condition.
    bool is_parity(bool& max, bool& odd, bool equiv = false) const;

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    // Return (true, m) if there exist some acceptance mark m that
    // does not satisfy the acceptance condition.  Return (false, 0U)
    // otherwise.
    std::pair<bool, acc_cond::mark_t> unsat_mark() const;

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  protected:
    bool check_fin_acceptance() const;

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  public:
    acc_code inf(mark_t mark) const
    {
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      return acc_code::inf(mark);
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    }

    acc_code inf(std::initializer_list<unsigned> vals) const
    {
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      return inf(mark_t(vals.begin(), vals.end()));
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    }

    acc_code inf_neg(mark_t mark) const
    {
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      return acc_code::inf_neg(mark);
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    }

    acc_code inf_neg(std::initializer_list<unsigned> vals) const
    {
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      return inf_neg(mark_t(vals.begin(), vals.end()));
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    }

    acc_code fin(mark_t mark) const
    {
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      return acc_code::fin(mark);
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    }

    acc_code fin(std::initializer_list<unsigned> vals) const
    {
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      return fin(mark_t(vals.begin(), vals.end()));
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    }

    acc_code fin_neg(mark_t mark) const
    {
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      return acc_code::fin_neg(mark);
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    }

    acc_code fin_neg(std::initializer_list<unsigned> vals) const
    {
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      return fin_neg(mark_t(vals.begin(), vals.end()));
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    }

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    unsigned add_sets(unsigned num)
    {
      if (num == 0)
	return -1U;
      unsigned j = num_;
      num_ += num;
      if (num_ > 8 * sizeof(mark_t::id))
	throw std::runtime_error("Too many acceptance sets used.");
      all_ = all_sets_();
      return j;
    }

    unsigned add_set()
    {
      return add_sets(1);
    }

    mark_t mark(unsigned u) const
    {
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      assert(u < num_sets());
      return 1U << u;
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    }

    mark_t comp(mark_t l) const
    {
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      return all_ ^ l.id;
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    }

    mark_t all_sets() const
    {
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      return all_;
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    }

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    bool accepting(mark_t inf) const
    {
      return code_.accepting(inf);
    }
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    bool inf_satisfiable(mark_t inf) const
    {
      return code_.inf_satisfiable(inf);
    }
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    mark_t accepting_sets(mark_t inf) const;
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    std::ostream& format(std::ostream& os, mark_t m) const
    {
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      auto a = m;
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      if (a == 0U)
	return os;
      return os << m;
    }

    std::string format(mark_t m) const
    {
      std::ostringstream os;
      format(os, m);
      return os.str();
    }

    unsigned num_sets() const
    {
      return num_;
    }

    template<class iterator>
    mark_t useless(iterator begin, iterator end) const
    {
      mark_t::value_t u = 0U;	// The set of useless marks.
      for (unsigned x = 0; x < num_; ++x)
	{
	  // Skip marks that are already known to be useless.
	  if (u & (1 << x))
	    continue;
	  unsigned all = all_ ^ (u | (1 << x));
	  for (iterator y = begin; y != end; ++y)
	    {
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	      auto v = y->id;
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	      if (v & (1 << x))
		{
		  all &= v;
		  if (!all)
		    break;
		}
	    }
	  u |= all;
	}
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      return u;
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    }

  protected:
    mark_t::value_t all_sets_() const
    {
      if (num_ == 0)
	return 0;
      return -1U >> (8 * sizeof(mark_t::value_t) - num_);
    }

    unsigned num_;
    mark_t::value_t all_;
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    acc_code code_;
    bool uses_fin_acceptance_ = false;
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  };

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  SPOT_API
  std::ostream& operator<<(std::ostream& os, const acc_cond& acc);
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}

namespace std
{
  template<>
  struct hash<spot::acc_cond::mark_t>
  {
    size_t operator()(spot::acc_cond::mark_t m) const
    {
      std::hash<decltype(m.id)> h;
      return h(m.id);
    }
  };
}