evaluation.hxx

// evaluation.hxx: this file is part of the Vaucanson project.
//
// Vaucanson, a generic library for finite state machines.
//
// Copyright (C) 2001, 2002, 2003, 2004 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_EVALUATION_HXX
# define VCSN_ALGORITHMS_EVALUATION_HXX

# include <vaucanson/algorithms/evaluation.hh>

# include <vaucanson/automata/concept/transducer_base.hh>

# include <vaucanson/algorithms/product.hh>
# include <vaucanson/algorithms/trim.hh>
# include <vaucanson/algorithms/standard.hh>
# include <vaucanson/algorithms/standard_of.hh>
# include <vaucanson/algorithms/aut_to_exp.hh>
# include <vaucanson/algorithms/extension.hh>
# include <vaucanson/algorithms/projection.hh>
# include <vaucanson/algorithms/aut_to_exp.hh>
# include <vaucanson/tools/usual_macros.hh>

namespace vcsn {

  template <typename SA, typename ST, typename SRET,
            typename Auto_t, typename Trans_t, typename Ret_t>
  void
  do_evaluation(const AutomataBase<SA>&,
                const TransducerBase<ST>&,
                const AutomataBase<SRET>&,
                const Auto_t& a,
                const Trans_t& t,
                Ret_t& ret)
  {
    Trans_t tt(t.structure());
    tt = extension(a, t);
    Trans_t pro(t.structure());
    pro = product(tt, t);
    pro = trim(pro);
    output_projection(pro, ret);
  }

  template<typename SA, typename TA, typename ST,
           typename TT, typename SRET, typename TRET>
  void
  evaluation(const Element<SA, TA>& a, const Element<ST, TT>& t,
             Element<SRET, TRET>& ret)
  {
    do_evaluation(a.structure(), t.structure(), ret.structure(), a, t, ret);
  }

  template<typename E, typename S, typename Trans_t, typename M>
  void
  do_partial_evaluation(const E& exp,
                        const TransducerBase<S>&,
                        const Trans_t& t,
                        M& state_exp_pair_set)
  {
    typedef typename Trans_t::value_t T;
    typedef typename output_projection_helper<S, T>::ret Auto_t;
    typedef typename Auto_t::set_t::series_set_t      Auto_series_set_t;
    typename Auto_t::set_t
      auto_structure(Auto_series_set_t(t.structure().series().semiring()));
    Auto_t tmp_auto(auto_structure);

    AUTOMATON_TYPES(Auto_t);
    monoid_elt_t empty = tmp_auto.series().monoid().empty_;
    standard_of(tmp_auto, exp.get(empty).value());
    partial_1(tmp_auto, t, state_exp_pair_set);
  }

  /* Input : an expression, a transducer.
   Output : a set of pair (hstate_t, expression)*/
  template<typename S1, typename T1,
           typename S2, typename T2,
           typename M>
  void
  partial_evaluation(const Element<S1, T1>& exp,
                     const Element<S2, T2>& trans,
                     M& state_exp_pair_set)
  {
    do_partial_evaluation(exp, trans.structure(), trans, state_exp_pair_set);
  }

  template<typename S, typename Auto_t, typename M, typename Chooser_t>
  void
  do_partial_elimination(const AutomataBase<S>&,
                         const Auto_t& a,
                         Chooser_t chooser,
                         M& state_exp_pair_set)
  {
    AUTOMATON_TYPES(Auto_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;

    Auto_t b = a;
    standardize(b);

    int num = b.final().size() + 1; // all final states and the initial state.

    while (int(b.states().size()) != num)
    {
      series_set_elt_t loop_sum(b.series());
      sums_t       in_sums, out_sums;
      typename sums_t::iterator f;
      q = chooser(b);
      if (b.is_initial(q) || b.is_final(q))
        continue;

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

        if (b.dst_of(*i) == q)
          loop_sum += b.series_of(*i);
        else if ((f = out_sums.find(b.dst_of(*i))) !=
                 out_sums.end())
          f->second += b.series_of(*i);
        else
          out_sums.insert(std::make_pair(b.dst_of(*i), b.series_of(*i)));
        b.del_transition(*i);
      }
      transitions.clear();
      // FIXME: use a new version of delta !
      b.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
        if ((f = in_sums.find(b.src_of(*i))) !=
            in_sums.end())
          f->second += b.series_of(*i);
        else
          in_sums.insert(std::make_pair(b.src_of(*i), b.series_of(*i)));
        b.del_transition(*i);
      }
      loop_sum.star();
      for_each_const_(sums_t, in, in_sums)
        for_each_const_(sums_t, out, out_sums)
      {
        series_set_elt_t res = in->second * loop_sum * out->second;
        b.add_series_transition(in->first, out->first, res);
      }
      b.del_state(q);
    }

    typedef std::map<hstate_t, series_set_elt_t>   se_map_t;
    typedef std::pair<hstate_t, series_set_elt_t>  state_exp_pair_t;
    se_map_t se_m;

    // maybe there are more than one transition comming to one final state
    // we must sum the labels
    for_each_transition(e, b)
    {
      hstate_t aim = b.dst_of(*e);
      typename se_map_t::iterator i = se_m.find(aim);
      if (i == se_m.end())
        se_m.insert(std::make_pair(aim,
                                   series_set_elt_t (b.structure().series(),
                                                     b.label_of(*e))));
      else
        i->second += b.label_of(*e);
    }

    for_each_final_state(p, b)
    {
      typename se_map_t::iterator i = se_m.find(*p);
      if (i != se_m.end())
        state_exp_pair_set.insert(std::make_pair(*p, i->second));
    }
  }

  /*------------.
  | elimination |
  `------------*/
  // preconditions :
  //   - hope that automaton's labels are sufficient to support "star"
  //     => in fact, generalized automaton are generally expected here.
  //

  template<typename A, typename T, typename M>
  void
  partial_elimination(const Element<A, T>& a,
                      M& state_exp_pair_set)
  {
    do_partial_elimination(a.structure(),
                           a,
                           DefaultChooser(),
                           state_exp_pair_set);
  }

  /* partial_1 */
  template<typename SA, typename ST,
           typename Auto_t, typename Trans_t,
           typename M>
  void
  do_partial_1(const AutomataBase<SA>&,
               const TransducerBase<ST>&,
               const Auto_t& a,
               const Trans_t& t,
               M& state_exp_pair_set)
  {
    typedef typename Trans_t::value_t T;
    typedef typename output_projection_helper<ST, T>::ret Auto_ret_t;
    typedef typename Auto_ret_t::set_t::series_set_t      Auto_ret_series_set_t;
    typename Auto_ret_t::set_t
      auto_structure(Auto_ret_series_set_t(t.structure().series().semiring()));

    AUTOMATON_TYPES_(Auto_t, a_);
    AUTOMATON_TYPES_(Trans_t, t_);
    AUTOMATON_TYPES_(Auto_ret_t, ret_);

    typedef std::map<hstate_t, std::pair<hstate_t, hstate_t> >
      state_pair_map_t;
    typedef std::map<hstate_t, hstate_t> state_state_map_t;
    typedef std::pair<hstate_t, ret_series_set_elt_t> se_pair_t;

    Trans_t tmp_trans(t.structure());
    tmp_trans = extension(a, t);

    Trans_t pro(t.structure());
    state_pair_map_t sp_m;
    pro = product(tmp_trans, t, sp_m);
    Auto_ret_t auto_p(auto_structure);
    std::map<hstate_t, hstate_t> proj_m;
    auto_p = output_projection(pro, proj_m);

    /* unset final all the final states of auto_p */
    auto_p.clear_final();

    /* for each state u of t, add one final state to 'auto_p' */
    state_state_map_t final_of, is_final_of;
    for(t_state_iterator u = t.states().begin(); u != t.states().end(); ++u)
    {
      hstate_t new_state = auto_p.add_state();
      final_of[*u] = new_state;
      is_final_of[new_state] = *u;
      auto_p.set_final(new_state);
    }

    for(a_state_iterator u = auto_p.states().begin();
        u != auto_p.states().end(); ++u)
    {
      if (!auto_p.is_final(*u))
      {
        hstate_t p = sp_m[proj_m[*u]].first;
        hstate_t q = sp_m[proj_m[*u]].second;

        if (tmp_trans.is_final(p))
          auto_p.add_spontaneous(*u, final_of[q]);
      }
    }

    M se;
    partial_elimination(auto_p, se);

    state_exp_pair_set.clear();
    for_each_(M, p, se)
    {
      se_pair_t my_pair = std::make_pair(is_final_of[(*p).first],
                                         p->second); // checking type compatibility
      state_exp_pair_set.insert(my_pair);
    }
  }

  template<typename SA, typename TA,
           typename ST, typename TT,
           typename M>
  void
  partial_1(const Element<SA, TA>& a,
            const Element<ST, TT>& t,
            M& state_exp_pair_set)
  {
    do_partial_1(a.structure(), t.structure(), a, t, state_exp_pair_set);
  }

  /* partial_2 */
  template<typename SA, typename ST,
           typename Auto_t, typename Trans_t,
           typename Exp>
  void
  do_partial_2(const AutomataBase<SA>&,
               const TransducerBase<ST>&,
               const Auto_t& a,
               const Trans_t& t,
               const hstate_t p,
               Exp& exp)
  {
    typedef typename Trans_t::value_t T;
    typedef typename output_projection_helper<ST, T>::ret    Auto_ret_t;
    typedef typename Auto_ret_t::set_t::series_set_t      Auto_ret_series_set_t;

    typename Auto_ret_t::set_t
      auto_structure(Auto_ret_series_set_t(t.structure().series().semiring()));

    Trans_t tt = t;
    tt.clear_initial();
    tt.set_initial(p);

    Trans_t tmp_trans(tt.structure());
    tmp_trans = extension(a, tt);

    Trans_t pro(t.structure());
    pro = trim(product(tmp_trans, tt));
    Auto_ret_t auto_p(auto_structure);
    auto_p = output_projection(pro);

    exp = aut_to_exp(auto_p);
  }

  template<typename SA, typename TA,
           typename ST, typename TT,
           typename Exp>
  void
  partial_2(const Element<SA, TA>& a,
            const Element<ST, TT>& t,
            const hstate_t p, Exp& exp)
  {
    do_partial_2(a.structure(), t.structure(), a, t, p, exp);
  }


  template<typename SA, typename ST,
           typename Auto_t, typename Trans_t,
           typename M>
  void
  do_partial_3(const AutomataBase<SA>&,
               const TransducerBase<ST>&,
               const Auto_t& a,
               const Trans_t& t,
               const hstate_t p,
               M& state_exp_pair_set)
  {
    Trans_t tt = t;
    tt.clear_initial();
    tt.set_initial(p);
    tt=trim(tt);
    partial_1(a, tt, state_exp_pair_set);
  }

  template<typename SA, typename TA,
           typename ST, typename TT,
           typename M>
  void
  partial_3(const Element<SA, TA>& a,
            const Element<ST, TT>& t,
            const hstate_t p,
            M& state_exp_pair_set)
  {
    do_partial_3(a.structure(), t.structure(), a, t, p, state_exp_pair_set);
  }

}

#endif // ! VCSN_ALGORITHMS_EVALUATION_HXX

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