rw_composition.hxx

// rw_composition.hxx: this file is part of the Vaucanson project.
//
// Vaucanson, a generic library for finite state machines.
//
// Copyright (C) 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009 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_RW_COMPOSITION_HXX
# define VCSN_ALGORITHMS_RW_COMPOSITION_HXX

# include <map>
# include <queue>
# include <set>

# include <vaucanson/algorithms/rw_composition.hh>
# include <vaucanson/algorithms/realtime.hh>
# include <vaucanson/automata/concept/transducer.hh>
// FIXME: The code for geometry computation must be enabled statically.
// (see product.hxx for some hints)
# include <vaucanson/automata/implementation/geometry.hh>
# include <vaucanson/algorithms/internal/evaluation.hh>

namespace vcsn
{
  template <typename U, typename Trans_t>
  void
  do_rw_composition(const TransducerBase<U>&,
                    const Trans_t& R,
                    const Trans_t& S,
                    Trans_t& T)
  {
    BENCH_TASK_SCOPED("rw_composition");

    // The second transducer must be realtime.
    precondition(is_realtime(S));

    // Type helpers.
    AUTOMATON_TYPES(Trans_t);
    typedef series_set_elt_t exp_t;
    typedef typename series_set_elt_t::semiring_elt_t output_exp_t;
    typedef std::set<std::pair<hstate_t, output_exp_t> > state_exp_pair_set_t;
    typedef typename std::map<hstate_t, typename Trans_t::geometry_t::coords_t>::const_iterator geom_iter_t;
    typedef std::pair<hstate_t, hstate_t> state_pair_t;
    typedef std::queue<state_pair_t> state_pair_queue_t;
    typedef std::map<state_pair_t, hstate_t> state_pair_map_t;
    typedef std::set<htransition_t> set_of_transitions_t;

    // Declare the main queue (FIFO).
    state_pair_queue_t queue;

    // We will reuse this structure many times:
    // each time we call partial_evaluation.
    // Do not forget to clear() it before the call.
    state_exp_pair_set_t sep_set;

    // Each time we create a new state in the output transducer
    // (say a pair (p, r)), we will add it to the following map
    // with the corresponding hstate_t, to speedup lookups.
    state_pair_map_t Tstates;

    // These variables help us to create the new state geometry.
    double xgeom;
    double ygeom;
    geom_iter_t iter;

    //
    // Part 1 (refer to the algorithm description - see header).
    // Initial states creation.
    //

    monoid_elt_t Ridentity = R.series().monoid().identity(SELECT(monoid_elt_value_t));
    monoid_elt_t Sidentity = S.series().monoid().identity(SELECT(monoid_elt_value_t));
    monoid_elt_t Tidentity = T.series().monoid().identity(SELECT(monoid_elt_value_t));

    for_all_const_initial_states (p, R)
    {
      // Hold the initial weight of the state p in R.
      // Warning: we suppose that the series on p is of the form: {w} 1, thus we
      // can access the weight directly. But R is not required to be realtime,
      // and there may be the series ({w} a) + ({z} b) on an initial state.
      output_exp_t E = R.get_initial(*p).get(Ridentity);

      for_all_const_initial_states (q, S)
      {
        // Hold the initial weight of the state q in S.
        // S is realtime, so we can access the weight directly.
        output_exp_t F = S.get_initial(*q).get(Sidentity);

        // Partial evaluation.
        sep_set.clear();
        partial_evaluation(E, S, *q, sep_set);

        // Iterates throughout the partial_evaluation output.
        for_all_const_(state_exp_pair_set_t, ig, sep_set)
        {
          // Construct the state representation (p, r).
          state_pair_t sp;
          sp.first = *p;
          sp.second = (*ig).first;

          if (Tstates.find(sp) == Tstates.end())
          {
            // (p, r) does not exists yet in the output transducer.

            // So we create it,
            hstate_t new_state = T.add_state();

            // add it the deduced geometry from p and r,
            iter = R.geometry().states().find(*p);
            if (iter != R.geometry().states().end())
              xgeom = (*iter).second.first;
            else
              xgeom = 0;
            iter = S.geometry().states().find(*q);
            if (iter != S.geometry().states().end())
              ygeom = (*iter).second.second;
            else
              ygeom = 0;
            T.geometry().states()[new_state] = std::make_pair(xgeom, ygeom);

            // store it in our lookup table,
            Tstates[sp] = new_state;

            // Set the initial weight. (see hypothesis on R)
            series_set_elt_t new_series(T.series());
            new_series.assoc(Tidentity, F * ((*ig).second));
            T.set_initial(new_state, new_series);

            // and finally push it in the queue.
            queue.push(sp);
          }
          else
          {
            // (p, r) has already been created: we only update its initial
            // weight.
            series_set_elt_t new_series(T.series());
            new_series.assoc(Tidentity, T.get_initial(Tstates[sp]).get(Tidentity) + F * ((*ig).second));
            T.set_initial(Tstates[sp], new_series);
          }
        } // ! for_all_const_state_exp_pair_set_t
      } // ! for_all_const_initial_states (S)
    } // ! for_all_const_initial_states (R)

    //
    // Part 2 (refer to the algorithm description - see header).
    // Main loop (runs until the queue is exhausted).
    //

    while (not queue.empty())
    {
      // Pop one state from the queue.
      const state_pair_t sp = queue.front();
      queue.pop();

      const hstate_t p = sp.first;
      const hstate_t q = sp.second;

      // Build (p, x, E, s).
      for (delta_iterator e(R.value(), p); !e.done(); e.next())
      {
        hstate_t s = R.dst_of(*e);
        exp_t E = R.series_of(*e);

        // R is not required to be realtime so we must iterate over the support
        // of E.
        for_all_const_(series_set_elt_t::support_t, y, E.supp())
        {
          const monoid_elt_t x(E.structure().monoid(), *y);

          // Partial evaluation.
          sep_set.clear();
          partial_evaluation(E.get(x), S, q, sep_set);

          for_all_const_(state_exp_pair_set_t, ig, sep_set)
          {
            // Construct the state representation (s, r).
            state_pair_t sp1;
            sp1.first = s;
            sp1.second = (*ig).first;

            if (Tstates.find(sp1) == Tstates.end())
            {
              // (s, r) does not exists yet in the output transducer.

              // So we create it,
              hstate_t new_state = T.add_state();

              // add it the deduced geometry from s and r,
              iter = R.geometry().states().find(sp1.first);
              if (iter != R.geometry().states().end())
                xgeom = (*iter).second.first;
              else
                xgeom = 0;
              iter = S.geometry().states().find(sp1.second);
              if (iter != S.geometry().states().end())
                ygeom = (*iter).second.second;
              else
                ygeom = 0;
              T.geometry().states()[new_state] = std::make_pair(xgeom, ygeom);

              // store it in our lookup table,
              Tstates[sp1] = new_state;

              // and finally push it in the queue.
              queue.push(sp1);
            }

            exp_t Gexp(R.structure().series());
            Gexp.assoc(x, (*ig).second);
            T.add_series_transition(Tstates[sp], Tstates[sp1], Gexp);
          } // ! for_all_const_state_exp_pair_set_t
        } // ! for_all_const_series_set_elt_t::support_t
      } // ! outgoing transitions from p in R

      // Handle final states.
      if (R.is_final(p))
      {
        // Partial evaluation.
        // The same hypothesis on the final states than for initial states hold.
        sep_set.clear();
        partial_evaluation(R.get_final(p).get(Ridentity), S, q, sep_set);

        for_all_const_(state_exp_pair_set_t, ig, sep_set)
        {
          const hstate_t r = (*ig).first;
          if (S.is_final(r))
          {
            series_set_elt_t new_series(T.series());
            // S is realtime so we can directly access the final weight.
            new_series.assoc(Tidentity, (*ig).second * S.get_final(r).get(Sidentity));
            T.set_final(Tstates[sp], new_series);
          }
        }
      } // ! is_final
    } // ! main loop
  }

  // Wrapper around do_rw_composition.
  template <typename S, typename T>
  void
  rw_composition(const Element<S, T>& lhs,
                 const Element<S, T>& rhs,
                 Element<S, T>& ret)
  {
    // Type helpers.
    typedef Element<S, T> auto_t;
    AUTOMATON_TYPES(auto_t);

    // We need to make sure RET is empty before passing it
    // to do_rw_composition(), therefore it won't work if
    // RET refers to the same automaton as LHS or RHS.
    precondition(&ret != &lhs);
    precondition(&ret != &rhs);

    // Remove all the state from ret.
    for_all_states (s, ret)
      ret.del_state(*s);

    do_rw_composition(lhs.structure(), lhs, rhs, ret);
  }

  // This wrapper creates a new automaton. No
  // special care needs be taken.
  template <typename S, typename T>
  Element<S, T>
  rw_composition(const Element<S, T>& lhs, const Element<S, T>& rhs)
  {
    // Create an empty automaton based on the lhs structure.
    Element<S, T> ret(lhs.structure());

    do_rw_composition(lhs.structure(), lhs, rhs, ret);
    return ret;
  }

} // ! vcsn

#endif // ! VCSN_ALGORITHMS_RW_COMPOSITION_HXX

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