dfa.cc

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/* -*- mode: C++; c-basic-offset: 2; indent-tabs-mode: nil -*- */
/*
 *  Main authors:
 *     Christian Schulte <schulte@gecode.org>
 *
 *  Copyright:
 *     Christian Schulte, 2004
 *
 *  Last modified:
 *     $Date: 2008-07-11 09:31:51 +0200 (Fri, 11 Jul 2008) $ by $Author: tack $
 *     $Revision: 7288 $
 *
 *  This file is part of Gecode, the generic constraint
 *  development environment:
 *     http://www.gecode.org
 *
 *  Permission is hereby granted, free of charge, to any person obtaining
 *  a copy of this software and associated documentation files (the
 *  "Software"), to deal in the Software without restriction, including
 *  without limitation the rights to use, copy, modify, merge, publish,
 *  distribute, sublicense, and/or sell copies of the Software, and to
 *  permit persons to whom the Software is furnished to do so, subject to
 *  the following conditions:
 *
 *  The above copyright notice and this permission notice shall be
 *  included in all copies or substantial portions of the Software.
 *
 *  THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
 *  EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
 *  MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
 *  NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE
 *  LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION
 *  OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION
 *  WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
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 */

#include "gecode/int.hh"

namespace Gecode { namespace Int { namespace Extensional {

  class TransByI_State {
  public:
    forceinline bool
    operator()(const DFA::Transition& x, const DFA::Transition& y) {
      return x.i_state < y.i_state;
    }
    forceinline static void
    sort(DFA::Transition t[], int n) {
      TransByI_State tbis;
      Support::quicksort<DFA::Transition,TransByI_State>(t,n,tbis);
    }
  };

  class TransBySymbol {
  public:
    forceinline bool
    operator()(const DFA::Transition& x, const DFA::Transition& y) {
      return x.symbol < y.symbol;
    }
    forceinline static void
    sort(DFA::Transition t[], int n) {
      TransBySymbol tbs;
      Support::quicksort<DFA::Transition,TransBySymbol>(t,n,tbs);
    }
  };

  class TransBySymbolI_State {
  public:
    forceinline bool
    operator()(const DFA::Transition& x, const DFA::Transition& y) {
      return ((x.symbol < y.symbol) ||
              ((x.symbol == y.symbol) && (x.i_state < y.i_state)));
    }
    forceinline static void
    sort(DFA::Transition t[], int n) {
      TransBySymbolI_State tbsi;
      Support::quicksort<DFA::Transition,TransBySymbolI_State>(t,n,tbsi);
    }
  };

  class TransByO_State {
  public:
    forceinline bool
    operator()(const DFA::Transition& x, const DFA::Transition& y) {
      return x.o_state < y.o_state;
    }
    forceinline static void
    sort(DFA::Transition t[], int n) {
      TransByO_State tbos;
      Support::quicksort<DFA::Transition,TransByO_State>(t,n,tbos);
    }
  };


  class StateGroup {
  public:
    int state;
    int group;
  };

  class StateGroupByGroup {
  public:
    forceinline bool
    operator()(const StateGroup& x, const StateGroup& y) {
      return ((x.group < y.group) ||
              ((x.group == y.group) && (x.state < y.state)));
    }
    static void
    sort(StateGroup sg[], int n) {
      StateGroupByGroup o;
      Support::quicksort<StateGroup,StateGroupByGroup>(sg,n,o);
    }
  };

  class GroupStates {
  public:
    StateGroup* fst;
    StateGroup* lst;
  };

  enum StateInfo {
    SI_NONE       = 0, 
    SI_FROM_START = 1, 
    SI_TO_FINAL   = 2, 
    SI_FINAL      = 4  
  };

}}}

namespace Gecode {

  DFA::DFA(int start, Transition t_spec[], int f_spec[], bool minimize) {
    using namespace Int;
    using namespace Extensional;
    // Compute number of states and transitions
    int n_states = start;
    int n_trans  = 0;
    for (Transition* t = &t_spec[0]; t->i_state >= 0; t++) {
      n_states = std::max(n_states,t->i_state);
      n_states = std::max(n_states,t->o_state);
      n_trans++;
    }
    for (int* f = &f_spec[0]; *f >= 0; f++)
      n_states = std::max(n_states,*f);
    n_states++;

    // Temporary structure for transitions
    GECODE_AUTOARRAY(Transition, trans, n_trans);
    for (int i = n_trans; i--; )
      trans[i] = t_spec[i];
    // Temporary structures for finals
    GECODE_AUTOARRAY(int,  final,    n_states+1);
    GECODE_AUTOARRAY(bool, is_final, n_states+1);
    int n_finals = 0;
    for (int i = n_states+1; i--; )
      is_final[i] = false;
    for (int* f = &f_spec[0]; *f != -1; f++) {
      is_final[*f]      = true;
      final[n_finals++] = *f;
    }

    if (minimize) {
      // Sort transitions by symbol and i_state
      TransBySymbolI_State::sort(trans, n_trans);
      GECODE_AUTOARRAY(Transition*, idx, n_trans+1);
      //  idx[i]...idx[i+1]-1 gives where transitions for symbol i start
      int n_symbols = 0;
      {
        int j = 0;
        while (j < n_trans) {
          idx[n_symbols++] = &trans[j];
          int s = trans[j].symbol;
          while ((j < n_trans) && (s == trans[j].symbol))
            j++;
        }
        idx[n_symbols] = &trans[j];
        assert(j == n_trans);
      }
      // Map states to groups
      GECODE_AUTOARRAY(int,         s2g,  n_states+1);
      GECODE_AUTOARRAY(StateGroup,  part, n_states+1);
      GECODE_AUTOARRAY(GroupStates, g2s,  n_states+1);
      // Initialize: final states is group one, all other group zero
      for (int i = n_states+1; i--; ) {
        part[i].state = i;
        part[i].group = is_final[i] ? 1 : 0;
        s2g[i]        = part[i].group;
      }
      // Important: the state n_state is the dead state, conceptually
      // if there is no transition for a symbol and input state, it is
      // assumed that there is an implicit transition to n_state

      // Set up the indexing data structure, sort by group
      StateGroupByGroup::sort(part,n_states+1);
      int n_groups;
      if (part[0].group == part[n_states].group) {
        // No final states, just one group
        g2s[0].fst = &part[0]; g2s[0].lst = &part[n_states+1];
        n_groups = 1;
      } else  {
        int i = 0;
        assert(part[0].group == 0);
        do i++; while (part[i].group == 0);
        g2s[0].fst = &part[0]; g2s[0].lst = &part[i];
        g2s[1].fst = &part[i]; g2s[1].lst = &part[n_states+1];
        n_groups = 2;
      }

      // Do the refinement
      {
        int m_groups;
        do {
          m_groups = n_groups;
          // Iterate over symbols
          for (int sidx = n_symbols; sidx--; ) {
            // Iterate over groups
            for (int g = n_groups; g--; ) {
              // Ignore singleton groups
              if (g2s[g].lst-g2s[g].fst > 1) {
                // Apply transitions to group states
                // This exploits that both transitions as well as
                // stategroups are sorted by (input) state
                Transition* t     = idx[sidx];
                Transition* t_lst = idx[sidx+1];
                for (StateGroup* sg = g2s[g].fst; sg<g2s[g].lst; sg++) {
                  while ((t < t_lst) && (t->i_state < sg->state))
                    t++;
                  // Compute group resulting from transition
                  if ((t < t_lst) && (t->i_state == sg->state))
                    sg->group = s2g[t->o_state];
                  else
                    sg->group = s2g[n_states]; // Go to dead state
                }
                // Sort group by groups from transitions
                StateGroupByGroup::sort(g2s[g].fst,
                                        static_cast<int>(g2s[g].lst-g2s[g].fst));
                // Group must be split?
                if (g2s[g].fst->group != (g2s[g].lst-1)->group) {
                  // Skip first group
                  StateGroup* sg = g2s[g].fst+1;
                  while ((sg-1)->group == sg->group)
                    sg++;
                  // Start splitting
                  StateGroup* lst = g2s[g].lst;
                  g2s[g].lst = sg;
                  while (sg < lst) {
                    s2g[sg->state] = n_groups;
                    g2s[n_groups].fst  = sg++;
                    while ((sg < lst) && ((sg-1)->group == sg->group)) {
                      s2g[sg->state] = n_groups; sg++;
                    }
                    g2s[n_groups++].lst = sg;
                  }
                }
              }
            }
          }
        } while (n_groups != m_groups);
        // New start state
        start = s2g[start];
        // Compute new final states
        n_finals = 0;
        for (int g = n_groups; g--; )
          for (StateGroup* sg = g2s[g].fst; sg < g2s[g].lst; sg++)
            if (is_final[sg->state]) {
              final[n_finals++] = g;
              break;
            }
        // Compute representatives
        GECODE_AUTOARRAY(int, s2r, n_states+1);
        for (int i = n_states+1; i--; )
          s2r[i] = -1;
        for (int g = n_groups; g--; )
          s2r[g2s[g].fst->state] = g;
        // Clean transitions
        int j = 0;
        for (int i = 0; i<n_trans; i++)
          if (s2r[trans[i].i_state] != -1) {
            trans[j].i_state = s2g[trans[i].i_state];
            trans[j].symbol  = trans[i].symbol;
            trans[j].o_state = s2g[trans[i].o_state];
            j++;
          }
        n_trans  = j;
        n_states = n_groups;
      }
    }

    // Do a reachability analysis for all states starting from start state
    GECODE_AUTOSTACK(int, -1, visit, n_states);
    GECODE_AUTOARRAY(int, state, n_states);
    for (int i=n_states; i--; )
      state[i] = SI_NONE;

    {
      // Sort all transitions according to i_state and create index structure
      //  idx[i]...idx[i+1]-1 gives where transitions for state i start
      TransByI_State::sort(trans, n_trans);
      GECODE_AUTOARRAY(Transition*, idx, n_states+1);
      {
        int j = 0;
        for (int i=0; i<n_states; i++) {
          idx[i] = &trans[j];
          while ((j < n_trans) && (i == trans[j].i_state))
            j++;
        }
        idx[n_states] = &trans[j];
        assert(j == n_trans);
      }

      state[start] = SI_FROM_START;
      visit.push(start);
      while (!visit.empty()) {
        int s = visit.pop();
        for (Transition* t = idx[s]; t < idx[s+1]; t++)
          if (!(state[t->o_state] & SI_FROM_START)) {
            state[t->o_state] |= SI_FROM_START;
            visit.push(t->o_state);
          }
      }
    }

    // Do a reachability analysis for all states to a final state
    {
      // Sort all transitions according to o_state and create index structure
      //  idx[i]...idx[i+1]-1 gives where transitions for state i start
      TransByO_State::sort(trans, n_trans);
      GECODE_AUTOARRAY(Transition*, idx, n_states+1);
      {
        int j = 0;
        for (int i=0; i<n_states; i++) {
          idx[i] = &trans[j];
          while ((j < n_trans) && (i == trans[j].o_state))
            j++;
        }
        idx[n_states] = &trans[j];
        assert(j == n_trans);
      }

      for (int i = n_finals; i--; ) {
        state[final[i]] |= (SI_TO_FINAL | SI_FINAL);
        visit.push(final[i]);
      }
      while (!visit.empty()) {
        int s = visit.pop();
        for (Transition* t = idx[s]; t < idx[s+1]; t++)
          if (!(state[t->i_state] & SI_TO_FINAL)) {
            state[t->i_state] |= SI_TO_FINAL;
            visit.push(t->i_state);
          }
      }
    }

    // Now all reachable states are known (also the final ones)
    GECODE_AUTOARRAY(int, re, n_states);
    for (int i = n_states; i--; )
      re[i] = -1;

    // Renumber states
    int m_states = 0;
    // Start state gets zero
    re[start] = m_states++;

    // Renumber final states
    for (int i = n_states; i--; )
      if ((state[i] == (SI_FINAL | SI_FROM_START | SI_TO_FINAL)) && (re[i] < 0))
        re[i] = m_states++;
    // If start state is final, final states start from zero, otherwise from one
    int final_fst = (state[start] & SI_FINAL) ? 0 : 1;
    int final_lst = m_states;
    // final_fst...final_lst-1 are the final states

    // Renumber remaining states
    for (int i = n_states; i--; )
      if ((state[i] == (SI_FROM_START | SI_TO_FINAL)) && (re[i] < 0))
        re[i] = m_states++;

    // Count number of remaining transitions
    int m_trans = 0;
    for (int i = n_trans; i--; )
      if ((re[trans[i].i_state] >= 0) && (re[trans[i].o_state] >= 0))
        m_trans++;

    // All done... Construct the automaton
    DFAI* d = new DFAI(m_trans);
    d->n_states  = m_states;
    d->n_trans   = m_trans;
    d->final_fst = final_fst;
    d->final_lst = final_lst;
    {
      int j = 0;
      Transition* r = &d->trans[0];
      for (int i = 0; i<n_trans; i++)
        if ((re[trans[i].i_state] >= 0) && (re[trans[i].o_state] >= 0)) {
          r[j].symbol  = trans[i].symbol;
          r[j].i_state = re[trans[i].i_state];
          r[j].o_state = re[trans[i].o_state];
          j++;
        }
      TransBySymbol::sort(r,m_trans);
    }
    {
      // Count number of symbols
      unsigned int n_symbols = 0;
      for (int i = 0; i<m_trans; ) {
        int s = d->trans[i++].symbol;
        n_symbols++;
        while ((i<m_trans) && (d->trans[i].symbol == s))
          i++;
      }
      d->n_symbols = n_symbols;
    }
    d->fill();
    object(d);
  }

  DFA::DFA(Reflection::VarMap& vm, Reflection::Arg* arg) {
    if (arg->isSharedReference()) {
      DFAI* d = 
        static_cast<DFAI*>(vm.getSharedObject(arg->toSharedReference()));
      object(d);
      return;
    }
    
    Reflection::IntArrayArg* a = arg->toSharedObject()->toIntArray();

    // All done... Construct the automaton

    int n_trans = (a->size() - 4) / 3;
    DFAI* d = new DFAI(n_trans);
    d->n_states  = (*a)[0];
    d->n_symbols = (*a)[1];
    d->final_fst = (*a)[2];
    d->final_lst = (*a)[3];
    d->n_trans   = n_trans;
    for (int i=0; i<n_trans; i++) {
      d->trans[i].i_state = (*a)[4+3*i+0];
      d->trans[i].symbol  = (*a)[4+3*i+1];
      d->trans[i].o_state = (*a)[4+3*i+2];
    }
    d->fill();
    object(d);    
    vm.putMasterObject(object());
  }

  Reflection::Arg*
  DFA::spec(Reflection::VarMap& vm) const {
    int sharedIndex = vm.getSharedIndex(object());
    if (sharedIndex >= 0)
      return Reflection::Arg::newSharedReference(sharedIndex);
    Reflection::IntArrayArg* a = 
      Reflection::Arg::newIntArray(static_cast<int>(4+3*n_transitions()));
    (*a)[0] = n_states();
    (*a)[1] = n_symbols();
    (*a)[2] = final_fst();
    (*a)[3] = final_lst();
    const DFAI* o = static_cast<DFAI*>(object());
    for (unsigned int i=0; i<n_transitions(); i++ ) {
      (*a)[4+3*i+0] = o->trans[i].i_state;
      (*a)[4+3*i+1] = o->trans[i].symbol;
      (*a)[4+3*i+2] = o->trans[i].o_state;
    }
    vm.putMasterObject(object());
    return Reflection::Arg::newSharedObject(a);    
  }

  SharedHandle::Object*
  DFA::DFAI::copy(void) const {
    DFAI* d = new DFAI(n_trans);
    d->n_states  = n_states;
    d->n_symbols = n_symbols;
    d->n_trans   = n_trans;
    d->final_fst = final_fst;
    d->final_lst = final_lst;
    memcpy(&d->trans[0], &trans[0], sizeof(Transition)*n_trans);
    d->fill();
    return d;
  }

  void
  DFA::DFAI::fill(void) {
    // Compute smallest logarithm larger than n_symbols
    n_log = 1;
    while (n_symbols >= static_cast<unsigned int>(1<<n_log))
      n_log++;
    // Allocate memory
    table = static_cast<HashEntry*>
      (Memory::malloc(sizeof(HashEntry)*(1<<n_log)));
    // Initialize table
    for (int i=(1<<n_log); i--; )
      table[i].fst = table[i].lst = NULL;
    int mask = (1 << n_log) - 1;
    // Enter transitions to table
    for (unsigned int i = 0; i<n_trans; ) {
      int s = trans[i].symbol;
      Transition* fst = &trans[i];
      i++;
      while ((i<n_trans) && (trans[i].symbol == s))
        i++;
      Transition* lst = &trans[i];
      // Enter with linear collision resolution
      int p = s & mask;
      while (table[p].fst != NULL)
        p = (p+1) & mask;
      table[p].symbol = s;
      table[p].fst    = fst;
      table[p].lst    = lst;
    }
  }

}

std::ostream&
operator<<(std::ostream& os, const Gecode::DFA& dfa) {
  os << "Start state: 0" << std::endl
     << "States:      0..." << dfa.n_states()-1 << std::endl
     << "Transitions:";
  for (int s = 0; s < static_cast<int>(dfa.n_states()); s++) {
    Gecode::DFA::Transitions t(dfa);
    int n = 0;
    while (t()) {
      if (t.i_state() == s) {
        if ((n % 4) == 0)
          os << std::endl << "\t";
        os << "[" << t.i_state() << "]"
           << "- " << t.symbol() << " >"
           << "[" << t.o_state() << "]  ";
        ++n;
      }
      ++t;
    }
  }
  os << std::endl << "Final states: "
     << std::endl
     << "\t[" << dfa.final_fst() << "] ... ["
     << dfa.final_lst()-1 << "]"
     << std::endl;
  return os;
}

// STATISTICS: int-prop