aut_to_exp.hxx

// aut_to_exp.hxx: this file is part of the Vaucanson project.
//
// Vaucanson, a generic library for finite state machines.
//
// Copyright (C) 2005 The Vaucanson Group.
//
// This program 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 2
// of the License, or (at your option) any later version.
//
// The complete GNU General Public Licence Notice can be found as the
// `COPYING' file in the root directory.
//
// The Vaucanson Group consists of people listed in the `AUTHORS' file.
//
#ifndef VCSN_ALGORITHMS_AUT_TO_EXP_HXX
# define VCSN_ALGORITHMS_AUT_TO_EXP_HXX

# include <vaucanson/algorithms/aut_to_exp.hh>

# include <vaucanson/automata/concept/handlers.hh>
# include <vaucanson/algorithms/normalized.hh>
# include <vaucanson/misc/usual_macros.hh>
# include <vaucanson/misc/contract.hh>
# include <vaucanson/misc/limits.hh>
# include <vaucanson/misc/random.hh>
# include <vaucanson/automata/concept/automata_base.hh>

# include <list>
# include <set>
# include <vector>

# include <stdlib.h>
# include <time.h>

namespace vcsn {

  /*---------------.
  | DefaultChooser |
  `---------------*/

  struct DefaultChooser
  {
      template <class Auto_>
      hstate_t
      operator()(const Auto_& a) const
      {
        assertion(a.states().size() > 0);
        typename Auto_::state_iterator s = a.states().begin();
        typename Auto_::state_iterator k = s;
        while ((k != a.states().end()) &&
               ((a.is_initial(*k)) || (a.is_final(*k))))
          ++k;
        s = k;
        return *s;
      }
  };


/*--------------.
| RandomChooser |
`--------------*/

  struct RandomChooser
  {
      template <class Auto_>
      hstate_t
      operator()(const Auto_& a) const
      {
        assertion(a.states().size() > 0);

        int n_init = 0;
        int n_final = 0;
        for (typename Auto_::state_iterator i = a.states().begin();
             i != a.states().end();
             ++i)
        {
          if (a.is_initial(*i))
            ++n_init;
          if (a.is_final(*i))
            ++n_final;
        }

        unsigned n = misc::random::generate((unsigned) 0,
                                               a.states().size() -
                                               (n_init + n_final));

        typename Auto_::state_iterator k = a.states().begin();
        unsigned kk = 0;
        while (kk <= n || k == a.states().end() ||
               ((a.is_initial(*k)) || (a.is_final(*k))))
        {
          if (k == a.states().end())
          {
            k = a.states().begin();
            continue;
          }
          ++k;
          ++kk;
        }
        return *k;
      }
  };


  /*----------------------------.
  |    Heuristic chooser:       |
  | Transition Number Heuristic |
  `----------------------------*/

  struct HChooser
  {
      template <class Auto_>
      hstate_t
      operator()(const Auto_& a) const
      {
        assertion(a.states().size() > 0);

        std::set<htransition_t> delta_in;
        std::set<htransition_t> delta_out;

        typename Auto_::state_iterator s = a.states().begin();
        unsigned int d_in = 0;
        unsigned int d_out = 0;
        unsigned int max = INT_MAX;
        bool has_loop = false;
        bool has_loop_old = false;

        for (typename Auto_::state_iterator i = a.states().begin();
             i != a.states().end();
             ++i)
        {
          if (a.is_final(*i) || a.is_initial(*i))
            continue;
          has_loop = false;

          a.deltac(delta_out, *i, delta_kind::transitions());
          a.rdeltac(delta_in, *i, delta_kind::transitions());
          for (typename std::set<htransition_t>::iterator j = delta_out.begin();
               j != delta_out.end();
               ++j)
            if (*i == a.dst_of(*j))
              has_loop = true;

          //FIXME : If the state has several loops
          if (has_loop)
            d_in = delta_in.size() - 1;
          else
            d_in = delta_in.size();
          d_out = delta_out.size();

          //We prefer to delete a state that has no loop transition
          if (d_in * d_out < max ||
              (d_in * d_out == max &&
               has_loop_old && not has_loop))
          {
            s = i;
            max = d_in * d_out;
            has_loop_old = has_loop;
          }
          delta_out.clear();
          delta_in.clear();
        }
        return *s;
      }
  };


  /*-------------------------.
  | Heuristic chooser:       |
  | from Delgado & Morais    |
  | (Proposed in CIAA 2004)  |
  `-------------------------*/
  struct DMChooser
  {
      template <class Auto_>
      hstate_t
      operator()(const Auto_& a) const
      {
        assertion(a.states().size() > 0);

        std::set<htransition_t> delta_in;
        std::set<htransition_t> delta_out;
        typename Auto_::state_iterator s = a.states().begin();

        unsigned int weight_min = INT_MAX;
        for (typename Auto_::state_iterator i = a.states().begin();
             i != a.states().end();
             ++i)
        {
          if (a.is_final(*i) || a.is_initial(*i))
            continue;
          unsigned int n_loops = 0;
          unsigned int in = 0;
          unsigned int out = 0;

          unsigned int weight = 0;

          delta_in.clear();
          delta_out.clear();
          a.deltac(delta_out, *i, delta_kind::transitions());
          a.rdeltac(delta_in, *i, delta_kind::transitions());

          for (typename std::set<htransition_t>::iterator j = delta_out.begin();
               j != delta_out.end();
               ++j)
            if (*i == a.dst_of(*j))
              ++n_loops;

          in = delta_in.size() - n_loops;
          out = delta_out.size() - n_loops;

          // Compute SUM(Win(k) * (Out - 1))
          for (typename std::set<htransition_t>::iterator j = delta_in.begin();
               j != delta_in.end();
               ++j)
            if (*i != a.dst_of(*j))
            {
              weight += a.series_value_of(*j).length() * (out - 1);
            }

          // Compute SUM(Wout(k) * (In - 1))
          for (typename std::set<htransition_t>::iterator j = delta_out.begin();
               j != delta_out.end();
               ++j)
            if (*i != a.dst_of(*j))
            {
              weight += a.series_value_of(*j).length() * (in - 1);
            }

          // Compute Wloop * (In * Out - 1)
          for (typename std::set<htransition_t>::iterator j = delta_out.begin();
               j != delta_out.end();
               ++j)
            if (*i == a.dst_of(*j))
            {
              weight += a.series_value_of(*j).length() * (in  * out - 1);
            }

          if (weight < weight_min)
          {
            s = i;
            weight_min = weight;
          }
        }
        return *s;
      }
  };




  /*------------.
  | ListChooser |
  `------------*/

  class ListChooser
  {
    public :
      ListChooser(const std::list<hstate_t>& l) :
        list_(l),
        pos_(l.begin())
      {}

      template <class Auto_>
      hstate_t operator() (const Auto_&)
      {
        assertion(pos_ != list_.end());
        return *pos_++;
      }

    private :
      std::list<hstate_t>       list_;
      std::list<hstate_t>::const_iterator pos_;
  };

  /*-----------.
  | aut_to_exp |
  `-----------*/

  template <class A_, typename Auto_, typename Chooser_>
  typename Auto_::series_set_elt_t
  do_in_aut_to_exp(const AutomataBase<A_>&  a_set,
                   Auto_&                   a,
                   Chooser_                 chooser)
  {
    AUTOMATON_TYPES(Auto_);
    typedef Auto_                                       automaton_t;
    typedef typename automaton_t::series_set_t          series_set_t;
    typedef typename automaton_t::series_set_elt_t      series_set_elt_t;

    typedef typename std::set<htransition_t>            htransition_set_t;
    typedef std::map<hstate_t, series_set_elt_t>        sums_t;

    typename htransition_set_t::const_iterator          i, j;
    hstate_t                                            q;
    htransition_set_t                                   transitions;
    std::list<htransition_t> transitions_to_remove;
    normalize_here(a);
    precondition(is_normalized(a));

    while (a.states().size() != 2)
    {
      series_set_elt_t loop_sum(a_set.series());
      sums_t       in_sums, out_sums;

      q = chooser(a);
      if (a.is_initial(q) || a.is_final(q))
        continue;

      transitions.clear();
      // FIXME: use a new version of delta!
      a.deltac(transitions, q, delta_kind::transitions());
      for (i = transitions.begin(); i != transitions.end(); i = j)
      {
        j = i; ++j;

        if (a.dst_of(*i) == q)
          loop_sum += a.series_of(*i);
        else
        {
          typename sums_t::iterator f = out_sums.find(a.dst_of(*i));
          if (f == out_sums.end())
            f = out_sums.insert
              (std::make_pair(a.dst_of(*i),
                              series_set_elt_t(a_set.series()))).first;
          f->second += a.series_of(*i);
        }
        a.del_transition(*i);
      }
      transitions.clear();
      // FIXME: use a new version of delta!
      a.rdeltac(transitions, q, delta_kind::transitions());
      for (i = transitions.begin(); i != transitions.end(); i = j)
      {
        j = i; ++j;
        // Here all loops have already been removed.
        typename sums_t::iterator f = in_sums.find(a.src_of(*i));
        if (f == in_sums.end())
          f = in_sums.insert
            (std::make_pair(a.src_of(*i),
                            series_set_elt_t(a_set.series()))).first;

        f->second += a.series_of(*i);
        a.del_transition(*i);
      }
      loop_sum.star();
      //Slow
      for_all_const_(sums_t, in, in_sums)
        for_all_const_(sums_t, out, out_sums)
      {
        series_set_elt_t res = in->second * loop_sum * out->second;
        a.add_series_transition(in->first, out->first, res);
      }
      a.del_state(q);
    }
    series_set_elt_t final(a_set.series());
    for_all_transitions(i, a)
      final += a.label_of(*i);
    return final;
  }

  /*-----------.
  | aut_to_exp |
  `-----------*/

  template<typename A, typename T, typename Chooser_>
  typename Element<A, T>::series_set_elt_t
  aut_to_exp(const Element<A, T>& a, const Chooser_& c)
  {
    Element<A, T> ret(a);
    return do_in_aut_to_exp(ret.structure(), ret, c);
  }

  template<typename A, typename T>
  typename Element<A, T>::series_set_elt_t
  aut_to_exp(const Element<A, T>& a)
  {
    return aut_to_exp(a, DefaultChooser());
  }

} // vcsn

#endif // ! VCSN_ALGORITHMS_AUT_TO_EXP_HXX

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