minimize.cc 15.2 KB
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// Copyright (C) 2010, 2011 Laboratoire de Recherche et Développement
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// de l'Epita (LRDE).
//
// 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 2 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 Spot; see the file COPYING.  If not, write to the Free
// Software Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA
// 02111-1307, USA.

#include <queue>
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#include <deque>
#include <set>
#include <list>
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#include <vector>
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#include "minimize.hh"
#include "ltlast/allnodes.hh"
#include "misc/hash.hh"
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#include "tgba/tgbaproduct.hh"
#include "tgba/tgbatba.hh"
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#include "tgbaalgos/powerset.hh"
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#include "tgbaalgos/gtec/gtec.hh"
#include "tgbaalgos/safety.hh"
#include "tgbaalgos/sccfilter.hh"
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#include "tgbaalgos/scc.hh"
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#include "tgbaalgos/ltl2tgba_fm.hh"
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#include "tgbaalgos/bfssteps.hh"
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namespace spot
{
  typedef Sgi::hash_set<const state*,
                        state_ptr_hash, state_ptr_equal> hash_set;
  typedef Sgi::hash_map<const state*, unsigned,
                        state_ptr_hash, state_ptr_equal> hash_map;

  // Given an automaton a, find all states that are not in "final" and add
  // them to the set "non_final".
  void init_sets(const tgba_explicit* a,
                 hash_set& final,
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                 hash_set& non_final)
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  {
    hash_set seen;
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    std::queue<const state*> tovisit;
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    // Perform breadth-first traversal.
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    const state* init = a->get_init_state();
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    tovisit.push(init);
    seen.insert(init);
    while (!tovisit.empty())
    {
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      const state* src = tovisit.front();
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      tovisit.pop();
      // Is the state final ?
      if (final.find(src) == final.end())
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	// No, add it to the set non_final
	non_final.insert(src->clone());
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      tgba_succ_iterator* sit = a->succ_iter(src);
      for (sit->first(); !sit->done(); sit->next())
      {
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        const state* dst = sit->current_state();
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        // Is it a new state ?
        if (seen.find(dst) == seen.end())
        {
          // Register the successor for later processing.
          tovisit.push(dst);
          seen.insert(dst);
        }
        else
          delete dst;
      }
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      delete sit;
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    }
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    while (!seen.empty())
      {
	hash_set::iterator i = seen.begin();
	const state* s = *i;
	seen.erase(i);
	delete s;
      }

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  }

  // From the base automaton and the list of sets, build the minimal
  // resulting automaton
  tgba_explicit_number* build_result(const tgba* a,
                                     std::list<hash_set*>& sets,
                                     hash_set* final)
  {
    // For each set, create a state in the resulting automaton.
    // For a state s, state_num[s] is the number of the state in the minimal
    // automaton.
    hash_map state_num;
    std::list<hash_set*>::iterator sit;
    unsigned num = 0;
    for (sit = sets.begin(); sit != sets.end(); ++sit)
    {
      hash_set::iterator hit;
      hash_set* h = *sit;
      for (hit = h->begin(); hit != h->end(); ++hit)
        state_num[*hit] = num;
      ++num;
    }
    typedef tgba_explicit_number::transition trs;
    tgba_explicit_number* res = new tgba_explicit_number(a->get_dict());
    // For each transition in the initial automaton, add the corresponding
    // transition in res.
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    if (!final->empty())
      res->declare_acceptance_condition(ltl::constant::true_instance());
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    for (sit = sets.begin(); sit != sets.end(); ++sit)
    {
      hash_set::iterator hit;
      hash_set* h = *sit;
      for (hit = h->begin(); hit != h->end(); ++hit)
      {
        const state* src = *hit;
        unsigned src_num = state_num[src];
        tgba_succ_iterator* succit = a->succ_iter(src);
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        bool accepting = (final->find(src) != final->end());
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        for (succit->first(); !succit->done(); succit->next())
        {
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          const state* dst = succit->current_state();
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          unsigned dst_num = state_num[dst];
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          delete dst;
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          trs* t = res->create_transition(src_num, dst_num);
          res->add_conditions(t, succit->current_condition());
          if (accepting)
            res->add_acceptance_condition(t, ltl::constant::true_instance());
        }
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        delete succit;
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      }
    }
    res->merge_transitions();
    const state* init_state = a->get_init_state();
    unsigned init_num = state_num[init_state];
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    delete init_state;
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    res->set_init_state(init_num);
    return res;
  }

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  namespace
  {

    struct wdba_search_acc_loop : public bfs_steps
    {
      wdba_search_acc_loop(const tgba* det_a,
			   unsigned scc_n, scc_map& sm,
			   power_map& pm, const state* dest)
	: bfs_steps(det_a), scc_n(scc_n), sm(sm), pm(pm), dest(dest)
      {
	seen.insert(dest);
      }

      virtual
      ~wdba_search_acc_loop()
      {
	hash_set::const_iterator i = seen.begin();
	while (i != seen.end())
	  {
	    hash_set::const_iterator old = i;
	    ++i;
	    delete *old;
	  }
      }

      virtual const state*
      filter(const state* s)
      {
	// Use the state from seen.
	hash_set::const_iterator i = seen.find(s);
	if (i == seen.end())
	  {
	    seen.insert(s);
	  }
	else
	  {
	    delete s;
	    s = *i;
	  }
	// Ignore states outside SCC #n.
	if (sm.scc_of_state(s) != scc_n)
	  return 0;
	return s;
      }

      virtual bool
      match(tgba_run::step&, const state* to)
      {
	return to == dest;
      }

      unsigned scc_n;
      scc_map& sm;
      power_map& pm;
      const state* dest;
      hash_set seen;
    };


    bool
    wdba_scc_is_accepting(const tgba_explicit_number* det_a, unsigned scc_n,
			  const tgba* orig_a, scc_map& sm, power_map& pm)
    {
      // Get some state from the SCC #n.
      const state* start = sm.one_state_of(scc_n)->clone();

      // Find a loop around START in SCC #n.
      wdba_search_acc_loop wsal(det_a, scc_n, sm, pm, start);
      tgba_run::steps loop;
      const state* reached = wsal.search(start, loop);
      assert(reached == start);
      (void)reached;

      // Build an automaton representing this loop.
      tgba_explicit_number loop_a(det_a->get_dict());
      tgba_run::steps::const_iterator i;
      int loop_size = loop.size();
      int n;
      for (n = 1, i = loop.begin(); n < loop_size; ++n, ++i)
	{
	  loop_a.create_transition(n - 1, n)->condition = i->label;
	  delete i->s;
	}
      assert(i != loop.end());
      loop_a.create_transition(n - 1, 0)->condition = i->label;
      delete i->s;
      assert(++i == loop.end());

      const state* loop_a_init = loop_a.get_init_state();
      assert(loop_a.get_label(loop_a_init) == 0);

      // Check if the loop is accepting in the original automaton.
      bool accepting = false;

      // Iterate on each original state corresponding to start.
      const power_map::power_state& ps = pm.states_of(det_a->get_label(start));
      for (power_map::power_state::const_iterator it = ps.begin();
	   it != ps.end() && !accepting; ++it)
	{
	  // Contrustruct a product between
	  // LOOP_A, and ORIG_A starting in *IT.

	  tgba* p = new tgba_product_init(&loop_a, orig_a,
					  loop_a_init, *it);

	  emptiness_check* ec = couvreur99(p);
	  emptiness_check_result* res = ec->check();

	  if (res)
	    accepting = true;
	  delete res;
	  delete ec;
	  delete p;
	}

      delete loop_a_init;
      return accepting;
    }

  }



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  tgba_explicit* minimize(const tgba* a, bool monitor)
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  {
    std::queue<hash_set*> todo;
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    // The list of equivalent states.
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    std::list<hash_set*> done;
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    hash_set* final = new hash_set;
    hash_set* non_final = new hash_set;
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    hash_map state_set_map;
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    tgba_explicit_number* det_a;

    {
      power_map pm;
      det_a = tgba_powerset(a, pm);
      if (!monitor)
	{
	  // For each SCC of the deterministic automaton, determine if
	  // it is accepting or not.
	  scc_map sm(det_a);
	  sm.build_map();
	  unsigned scc_count = sm.scc_count();
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	  std::vector<bool> accepting(scc_count);
	  // SCC are numbered in topological order
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	  for (unsigned n = 0; n < scc_count; ++n)
	    {
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	      bool acc = true;

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	      if (sm.trivial(n))
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		{
		  // Trivial SCCs are accepting if all their
		  // successors are accepting.

		  // This corresponds to the algorithm in Fig. 1 of
		  // "Efficient minimization of deterministic weak
		  // omega-automata" written by Christof Löding and
		  // published in Information Processing Letters 79
		  // (2001) pp 105--109.  Except we do not keep track
		  // of the actual color associated to each SCC.

		  const scc_map::succ_type& succ = sm.succ(n);
		  for (scc_map::succ_type::const_iterator i = succ.begin();
		       i != succ.end(); ++i)
		    {
		      if (!accepting[i->first])
			{
			  acc = false;
			  break;
			}
		    }
		}
	      else
		{
		  // Regular SCCs are accepting if any of their loop
		  // corresponds to an accepting
		  acc = wdba_scc_is_accepting(det_a, n, a, sm, pm);
		}

	      accepting[n] = acc;
	      if (acc)
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		{
		  std::list<const state*> l = sm.states_of(n);
		  std::list<const state*>::const_iterator il;
		  for (il = l.begin(); il != l.end(); ++il)
		    final->insert((*il)->clone());
		}
	    }
	}
    }
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    init_sets(det_a, *final, *non_final);
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    // Size of det_a
    unsigned size = final->size() + non_final->size();
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    // Use bdd variables to number sets.  set_num is the first variable
    // available.
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    unsigned set_num =
      det_a->get_dict()->register_anonymous_variables(size, det_a);
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    std::set<int> free_var;
    for (unsigned i = set_num; i < set_num + size; ++i)
      free_var.insert(i);
    std::map<int, int> used_var;

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    hash_set* final_copy;

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    if (!final->empty())
      {
	unsigned s = final->size();
	used_var[set_num] = s;
	free_var.erase(set_num);
	if (s > 1)
	  todo.push(final);
	else
	  done.push_back(final);
	for (hash_set::const_iterator i = final->begin();
	     i != final->end(); ++i)
	  state_set_map[*i] = set_num;
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	final_copy = new hash_set(*final);
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      }
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    else
      {
	final_copy = final;
      }

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    if (!non_final->empty())
      {
	unsigned s = non_final->size();
	unsigned num = set_num + 1;
	used_var[num] = s;
	free_var.erase(num);
	if (s > 1)
	  todo.push(non_final);
	else
	  done.push_back(non_final);
	for (hash_set::const_iterator i = non_final->begin();
	     i != non_final->end(); ++i)
	  state_set_map[*i] = num;
      }
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    else
      {
	delete non_final;
      }
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    // A bdd_states_map is a list of formulae (in a BDD form) associated with a
    // destination set of states.
    typedef std::list<std::pair<bdd, hash_set*> > bdd_states_map;
    // While we have unprocessed sets.
    while (!todo.empty())
    {
      // Get a set to process.
      hash_set* cur = todo.front();
      todo.pop();
      hash_set::iterator hi;
      bdd_states_map bdd_map;
      for (hi = cur->begin(); hi != cur->end(); ++hi)
      {
        const state* src = *hi;
        bdd f = bddfalse;
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        tgba_succ_iterator* si = det_a->succ_iter(src);
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        for (si->first(); !si->done(); si->next())
        {
          const state* dst = si->current_state();
          unsigned dst_set = state_set_map[dst];
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          delete dst;
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          f |= (bdd_ithvar(dst_set) & si->current_condition());
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        }
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        delete si;
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        bdd_states_map::iterator bsi;
        // Have we already seen this formula ?
        for (bsi = bdd_map.begin(); bsi != bdd_map.end() && bsi->first != f;
             ++bsi)
          continue;
        if (bsi == bdd_map.end())
        {
          // No, create a new set.
          hash_set* new_set = new hash_set;
          new_set->insert(src);
          bdd_map.push_back(std::make_pair<bdd, hash_set*>(f, new_set));
        }
        else
        {
          // Yes, add the current state to the set.
          hash_set* set = bsi->second;
          set->insert(src);
        }
      }
      bdd_states_map::iterator bsi = bdd_map.begin();
      // The set is minimal.
      if (bdd_map.size() == 1)
        done.push_back(bsi->second);
      else
      {
        for (; bsi != bdd_map.end(); ++bsi)
        {
          hash_set* set = bsi->second;
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          // Free the number associated to these states.
	  unsigned num = state_set_map[*set->begin()];
	  assert(used_var.find(num) != used_var.end());
	  unsigned left = (used_var[num] -= set->size());
	  // Make sure LEFT does not become negative (hence bigger
	  // than SIZE when read as unsigned)
	  assert(left < size);
	  if (left == 0)
	    {
	      used_var.erase(num);
	      free_var.insert(num);
	    }
	  // Pick a free number
	  assert(!free_var.empty());
	  num = *free_var.begin();
	  free_var.erase(free_var.begin());
	  used_var[num] = set->size();
          for (hash_set::iterator hit = set->begin(); hit != set->end(); ++hit)
	    state_set_map[*hit] = num;
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          // Trivial sets can't be splitted any further.
          if (set->size() == 1)
            done.push_back(set);
          else
            todo.push(set);
        }
      }
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      delete cur;
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    }
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    // Build the result.
    tgba_explicit_number* res = build_result(det_a, done, final_copy);

    // Free all the allocated memory.
    delete final_copy;
    hash_map::iterator hit;
    for (hit = state_set_map.begin(); hit != state_set_map.end(); ++hit)
      delete hit->first;
    std::list<hash_set*>::iterator it;
    for (it = done.begin(); it != done.end(); ++it)
      delete *it;
    delete det_a;

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    return res;
  }
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  const tgba*
  minimize_obligation(const tgba* aut_f,
		      const ltl::formula* f, const tgba* aut_neg_f)
  {
    // WDBA minimization
    tgba* min_aut_f = minimize(aut_f);

    // If aut_f is a safety automaton, the WDBA minimization must be
    // correct.
    if (is_safety_automaton(aut_f))
      {
	return min_aut_f;
      }

    if (!f && !aut_neg_f)
      {
	// We do not now if the minimization is safe.
	return 0;
      }

    const tgba* to_free = 0;

    // Build negation automaton if not supplied.
    if (!aut_neg_f)
      {
	assert(f);

	ltl::formula* neg_f = ltl::unop::instance(ltl::unop::Not, f->clone());
	aut_neg_f = ltl_to_tgba_fm(neg_f, aut_f->get_dict());
	neg_f->destroy();

	// Remove useless SCCs.
	const tgba* tmp = scc_filter(aut_neg_f, true);
	delete aut_neg_f;
	to_free = aut_neg_f = tmp;
      }

    // If the negation is a safety automaton, then the
    // minimization is correct.
    if (is_safety_automaton(aut_neg_f))
      {
	delete to_free;
	return min_aut_f;
      }

    bool ok = false;

    tgba* p = new tgba_product(min_aut_f, aut_neg_f);
    emptiness_check* ec = couvreur99(p);
    emptiness_check_result* res = ec->check();
    if (!res)
      {
	delete ec;
	delete p;
	tgba* min_aut_neg_f = minimize(aut_neg_f);
	tgba* p = new tgba_product(aut_f, min_aut_neg_f);
	emptiness_check* ec = couvreur99(p);
	res = ec->check();

	if (!res)
	  // Finally, we are now sure that it was safe
	  // to minimize the automaton.
	  ok = true;

	delete res;
	delete ec;
	delete p;
	delete min_aut_neg_f;
      }
    else
      {
	delete res;
	delete ec;
	delete p;
      }
    delete to_free;

    if (ok)
      return min_aut_f;
    delete min_aut_f;
    return aut_f;
  }
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}