ltl2tgba_fm.cc

// Copyright (C) 2003, 2004  Laboratoire d'Informatique de Paris 6 (LIP6),
// dpartement Systmes Rpartis Coopratifs (SRC), Universit Pierre
// et Marie Curie.
//
// 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 "misc/hash.hh"
#include "misc/bddalloc.hh"
#include "misc/bddlt.hh"
#include "misc/minato.hh"
#include "ltlast/visitor.hh"
#include "ltlast/allnodes.hh"
#include "ltlvisit/lunabbrev.hh"
#include "ltlvisit/nenoform.hh"
#include "ltlvisit/destroy.hh"
#include "ltlvisit/tostring.hh"
#include <cassert>

#include "tgba/tgbabddconcretefactory.hh"
#include "ltl2tgba_fm.hh"

namespace spot
{
  using namespace ltl;

  namespace
  {

    // Helper dictionary.  We represent formulae using BDDs to
    // simplify them, and then translate BDDs back into formulae.
    //
    // The name of the variables are inspired from Couvreur's FM paper.
    //   "a" variables are promises (written "a" in the paper)
    //   "next" variables are X's operands (the "r_X" variables from the paper)
    //   "var" variables are atomic propositions.
    class translate_dict
    {
    public:

      translate_dict(bdd_dict* dict)
	: dict(dict),
	  a_set(bddtrue),
	  var_set(bddtrue),
	  next_set(bddtrue)
      {
      }

      ~translate_dict()
      {
	fv_map::iterator i;
	for (i = next_map.begin(); i != next_map.end(); ++i)
	  destroy(i->first);
	dict->unregister_all_my_variables(this);
      }

      bdd_dict* dict;

      /// Formula-to-BDD-variable maps.
      typedef Sgi::hash_map<const formula*, int,
			    ptr_hash<formula> > fv_map;
      /// BDD-variable-to-formula maps.
      typedef Sgi::hash_map<int, const formula*> vf_map;

      fv_map next_map;	       ///< Maps "Next" variables to BDD variables
      vf_map next_formula_map; ///< Maps BDD variables to "Next" variables

      bdd a_set;
      bdd var_set;
      bdd next_set;

      int
      register_proposition(const formula* f)
      {
	int num = dict->register_proposition(f, this);
	var_set &= bdd_ithvar(num);
	return num;
      }

      int
      register_a_variable(const formula* f)
      {
	int num = dict->register_acceptance_variable(f, this);
	a_set &= bdd_ithvar(num);
	return num;
      }

      int
      register_next_variable(const formula* f)
      {
	int num;
	// Do not build a Next variable that already exists.
	fv_map::iterator sii = next_map.find(f);
	if (sii != next_map.end())
	  {
	    num = sii->second;
	  }
	else
	  {
	    f = clone(f);
	    num = dict->register_anonymous_variables(1, this);
	    next_map[f] = num;
	    next_formula_map[num] = f;
	  }
	next_set &= bdd_ithvar(num);
	return num;
      }

      std::ostream&
      dump(std::ostream& os) const
      {
	fv_map::const_iterator fi;
	os << "Next Variables:" << std::endl;
	for (fi = next_map.begin(); fi != next_map.end(); ++fi)
	{
	  os << "  " << fi->second << ": Next[";
	  to_string(fi->first, os) << "]" << std::endl;
	}
	os << "Shared Dict:" << std::endl;
	dict->dump(os);
	return os;
      }

      formula*
      var_to_formula(int var) const
      {
	vf_map::const_iterator isi = next_formula_map.find(var);
	if (isi != next_formula_map.end())
	  return clone(isi->second);
	isi = dict->acc_formula_map.find(var);
	if (isi != dict->acc_formula_map.end())
	  return clone(isi->second);
	isi = dict->var_formula_map.find(var);
	if (isi != dict->var_formula_map.end())
	  return clone(isi->second);
	assert(0);
      }

      formula*
      conj_bdd_to_formula(bdd b)
      {
	if (b == bddfalse)
	  return constant::false_instance();
	multop::vec* v = new multop::vec;
	while (b != bddtrue)
	  {
	    int var = bdd_var(b);
	    formula* res = var_to_formula(var);
	    bdd high = bdd_high(b);
	    if (high == bddfalse)
	      {
		res = unop::instance(unop::Not, res);
		b = bdd_low(b);
	      }
	    else
	      {
		assert(bdd_low(b) == bddfalse);
		b = high;
	      }
	    assert(b != bddfalse);
	    v->push_back(res);
	  }
	return multop::instance(multop::And, v);
      }

      const formula*
      bdd_to_formula(bdd f)
      {
	if (f == bddfalse)
	  return constant::false_instance();

	multop::vec* v = new multop::vec;

	minato_isop isop(f);
	bdd cube;
	while ((cube = isop.next()) != bddfalse)
	  v->push_back(conj_bdd_to_formula(cube));

	return multop::instance(multop::Or, v);
      }

      void
      conj_bdd_to_acc(tgba_explicit* a, bdd b, tgba_explicit::transition* t)
      {
	assert(b != bddfalse);
	while (b != bddtrue)
	  {
	    int var = bdd_var(b);
	    bdd high = bdd_high(b);
	    if (high == bddfalse)
	      {
		// Simply ignore negated acceptance variables.
		b = bdd_low(b);
	      }
	    else
	      {
		formula* ac = var_to_formula(var);

		if (! a->has_acceptance_condition(ac))
		  a->declare_acceptance_condition(clone(ac));
		a->add_acceptance_condition(t, ac);
		b = high;
	      }
	    assert(b != bddfalse);
	  }
      }
    };


    // The rewrite rules used here are adapted from Jean-Michel
    // Couvreur's FM paper.
    class ltl_trad_visitor: public const_visitor
    {
    public:
      ltl_trad_visitor(translate_dict& dict)
	: dict_(dict)
      {
      }

      virtual
      ~ltl_trad_visitor()
      {
      }

      bdd result() const
      {
	return res_;
      }

      void
      visit(const atomic_prop* node)
      {
	res_ = bdd_ithvar(dict_.register_proposition(node));
      }

      void
      visit(const constant* node)
      {
	switch (node->val())
	  {
	  case constant::True:
	    res_ = bddtrue;
	    return;
	  case constant::False:
	    res_ = bddfalse;
	    return;
	  }
	/* Unreachable code.  */
	assert(0);
      }

      void
      visit(const unop* node)
      {
	switch (node->op())
	  {
	  case unop::F:
	    {
	      // r(Fy) = r(y) + a(y)r(XFy)
	      const formula* child = node->child();
	      bdd y = recurse(child);
	      int a = dict_.register_a_variable(child);
	      int x = dict_.register_next_variable(node);
	      res_ = y | (bdd_ithvar(a) & bdd_ithvar(x));
	      return;
	    }
	  case unop::G:
	    {
	      // The paper suggests that we optimize GFy
	      // as
	      //   r(GFy) = (r(y) + a(y))r(XGFy)
	      // instead of
	      //   r(GFy) = (r(y) + a(y)r(XFy)).r(XGFy)
	      // but this is just a particular case
	      // of the "merge all states with the same
	      // symbolic rewriting" optimization we do later.
	      // (r(Fy).r(GFy) and r(GFy) have the same symbolic
	      // rewriting.)  Let's keep things simple here.

	      // r(Gy) = r(y)r(XGy)
	      const formula* child = node->child();
	      int x = dict_.register_next_variable(node);
	      bdd y = recurse(child);
	      res_ = y & bdd_ithvar(x);
	      return;
	    }
	  case unop::Not:
	    {
	      // r(!y) = !r(y)
	      res_ = bdd_not(recurse(node->child()));
	      return;
	    }
	  case unop::X:
	    {
	      // r(Xy) = Next[y]
	      int x = dict_.register_next_variable(node->child());
	      res_ = bdd_ithvar(x);
	      return;
	    }
	  }
	/* Unreachable code.  */
	assert(0);
      }

      void
      visit(const binop* node)
      {
	bdd f1 = recurse(node->first());
	bdd f2 = recurse(node->second());

	switch (node->op())
	  {
	    // r(f1 logical-op f2) = r(f1) logical-op r(f2)
	  case binop::Xor:
	    res_ = bdd_apply(f1, f2, bddop_xor);
	    return;
	  case binop::Implies:
	    res_ = bdd_apply(f1, f2, bddop_imp);
	    return;
	  case binop::Equiv:
	    res_ = bdd_apply(f1, f2, bddop_biimp);
	    return;
	  case binop::U:
	    {
	      // r(f1 U f2) = r(f2) + a(f2)r(f1)r(X(f1 U f2))
	      int a = dict_.register_a_variable(node->second());
	      int x = dict_.register_next_variable(node);
	      res_ = f2 | (bdd_ithvar(a) & f1 & bdd_ithvar(x));
	      return;
	    }
	  case binop::R:
	    {
	      // r(f1 R f2) = r(f1)r(f2) + r(f2)r(X(f1 U f2))
	      int x = dict_.register_next_variable(node);
	      res_ = (f1 & f2) | (f2 & bdd_ithvar(x));
	      return;
	    }
	  }
	/* Unreachable code.  */
	assert(0);
      }

      void
      visit(const multop* node)
      {
	int op = -1;
	switch (node->op())
	  {
	  case multop::And:
	    op = bddop_and;
	    res_ = bddtrue;
	    break;
	  case multop::Or:
	    op = bddop_or;
	    res_ = bddfalse;
	    break;
	  }
	assert(op != -1);
	unsigned s = node->size();
	for (unsigned n = 0; n < s; ++n)
	  {
	    res_ = bdd_apply(res_, recurse(node->nth(n)), op);
	  }
      }

      bdd
      recurse(const formula* f)
      {
	ltl_trad_visitor v(dict_);
	f->accept(v);
	return v.result();
      }


    private:
      translate_dict& dict_;
      bdd res_;
    };

  }

  tgba_explicit*
  ltl_to_tgba_fm(const formula* f, bdd_dict* dict,
		 bool exprop, bool symb_merge)
  {
    // Normalize the formula.  We want all the negations on
    // the atomic propositions.  We also suppress logic
    // abbreviations such as <=>, =>, or XOR, since they
    // would involve negations at the BDD level.
    formula* f1 = unabbreviate_logic(f);
    formula* f2 = negative_normal_form(f1);
    destroy(f1);

    std::set<const formula*> formulae_seen;
    std::set<const formula*> formulae_to_translate;
    // Map a representation of successors to a canonical formula.
    // We do this because many formulae (such as `aR(bRc)' and
    // `aR(bRc).(bRc)') are equivalent, and are trivially identified
    // by looking at the set of successors.
    typedef std::map<bdd, const formula*, bdd_less_than> succ_to_formula;
    succ_to_formula canonical_succ;

    translate_dict d(dict);
    ltl_trad_visitor v(d);

    formulae_seen.insert(f2);
    formulae_to_translate.insert(f2);

    tgba_explicit* a = new tgba_explicit(dict);

    a->set_init_state(to_string(f2));

    while (!formulae_to_translate.empty())
      {
	// Pick one formula.
	const formula* f = *formulae_to_translate.begin();
	formulae_to_translate.erase(formulae_to_translate.begin());

	// Translate it into a BDD to simplify it.
	// FIXME: Currently the same formula can be converted into a
	// BDD twice.  Once in the symb_merge block below, and then
	// once here.
	f->accept(v);
	bdd res = v.result();
	succ_to_formula::iterator cs = canonical_succ.find(res);
	if (cs == canonical_succ.end())
	  canonical_succ[res] = clone(f);

	std::string now = to_string(f);

	// We used to factor only Next and A variables while computing
	// prime implicants, with
	//    minato_isop isop(res, d.next_set & d.a_set);
	// in order to obtain transitions with formulae of atomic
	// proposition directly, but unfortunately this led to strange
	// factorizations.  For instance f U g was translated as
	//     r(f U g) = g + a(g).r(X(f U g)).(f + g)
	// instead of just
	//     r(f U g) = g + a(g).r(X(f U g)).f
	// Of course both formulae are logically equivalent, but the
	// latter is "more deterministic" than the former, so it should
	// be preferred.
	//
	// Therefore we now factor all variables.  This may lead to more
	// transitions than necessary (e.g.,  r(f + g) = f + g  will be
	// coded as two transitions), but we later merge all transitions
	// with same source/destination and acceptance conditions.  This
	// is the goal of the `dests' hash.
	//
	// Note that this is still not optimal.  For instance it is
	// better to encode `f U g' as
	//     r(f U g) = g + a(g).r(X(f U g)).f.!g
	// because that leads to a deterministic automaton.  In order
	// to handle this, we take the conditions of any transition
	// going to true (it's `g' here), and remove it from the other
	// transitions.
	//
	// In `exprop' mode, considering all possible combinations of
	// outgoing propositions generalizes the above trick.

	typedef std::map<bdd, bdd, bdd_less_than> prom_map;
	typedef Sgi::hash_map<const formula*, prom_map, ptr_hash<formula> >
	  dest_map;
	dest_map dests;

	// Compute all outgoing arcs.

	// If EXPROP is set, we will refine the symbolic
	// representation of the successors for all combinations of
	// the atomic properties involved in the formula.
	// VAR_SET is the set of these properties.
	bdd var_set = bdd_existcomp(bdd_support(res), d.var_set);
	// ALL_PROPS is the combinations we have yet to consider.
	// We used to start with `all_props = bddtrue', but it is
	// more efficient to start with the set of all satisfiable
	// variables combinations.
	bdd all_props = bdd_existcomp(res, d.var_set);
	while (all_props != bddfalse)
	  {
	    bdd one_prop_set =
	      exprop ? bdd_satoneset(all_props, var_set, bddtrue) : bddtrue;
	    all_props -= one_prop_set;
	    minato_isop isop(res & one_prop_set);
	    bdd cube;
	    while ((cube = isop.next()) != bddfalse)
	      {
		const formula* dest =
		  d.conj_bdd_to_formula(bdd_existcomp(cube, d.next_set));

		// If we already know a state with the same successors,
		// use it in lieu of the current one.  (See the comments
		// for canonical_succ.)  We need to do this only for new
		// destinations.
		if (symb_merge
		    && formulae_seen.find(dest) == formulae_seen.end())
		  {
		    dest->accept(v);
		    bdd succbdd = v.result();
		    succ_to_formula::iterator cs =
		      canonical_succ.find(succbdd);
		    if (cs != canonical_succ.end())
		      {
			destroy(dest);
			dest = clone(cs->second);
		      }
		    else
		      {
			canonical_succ[succbdd] = clone(dest);
		      }
		  }

		bdd promises = bdd_existcomp(cube, d.a_set);
		bdd conds =
		  exprop ? one_prop_set : bdd_existcomp(cube, var_set);

		dest_map::iterator i = dests.find(dest);
		if (i == dests.end())
		  {
		    dests[dest][promises] = conds;
		  }
		else
		  {
		    i->second[promises] |= conds;
		    destroy(dest);
		  }
	      }
	  }

	// Check for an arc going to 1 (True).  Register it first, that
	// way it will be explored before the other during the model
	// checking.
	dest_map::const_iterator i = dests.find(constant::true_instance());
	// COND_FOR_TRUE is the conditions of the True arc, so when
	// can remove them from all other arcs.  It might sounds that
	// this is not needed when exprop is used, but in fact it is
	// complementary.
	//
	// Consider
	//   f = r(X(1) R p) = p.(1 + r(X(1) R p))
	// with exprop the two outgoing arcs would be
        //         p                  p
	//     f ----> 1       f ----------> 1
	//
	// where in fact we could output
        //         p
	//     f ----> 1
	//
	// because there is no point in looping on f if we can go to 1.
	bdd cond_for_true = bddfalse;
	if (i != dests.end())
	  {
	    // Transitions going to 1 (true) are not expected to make
	    // any promises.
	    assert(i->second.size() == 1);
	    prom_map::const_iterator j = i->second.find(bddtrue);
	    assert(j != i->second.end());

	    cond_for_true = j->second;
	    tgba_explicit::transition* t =
	      a->create_transition(now, constant::true_instance()->val_name());
	    a->add_condition(t, d.bdd_to_formula(cond_for_true));
	  }
	// Register other transitions.
	for (i = dests.begin(); i != dests.end(); ++i)
	  {
	    const formula* dest = i->first;
	    // The cond_for_true optimization can cause some
	    // transitions to be removed.  So we have to remember
	    // whether a formula is actually reachable.
	    bool reachable = false;

	    if (dest != constant::true_instance())
	      {
		std::string next = to_string(dest);
		for (prom_map::const_iterator j = i->second.begin();
		     j != i->second.end(); ++j)
		  {
		    bdd cond = j->second - cond_for_true;
		    if (cond == bddfalse) // Skip false transitions.
		      continue;
		    tgba_explicit::transition* t =
		      a->create_transition(now, next);
		    a->add_condition(t, d.bdd_to_formula(cond));
		    d.conj_bdd_to_acc(a, j->first, t);
		    reachable = true;
		  }
	      }
	    else
	      {
		// "1" is reachable.
		reachable = true;
	      }
	    if (reachable
		&& formulae_seen.find(dest) == formulae_seen.end())
	      {
		formulae_seen.insert(dest);
		formulae_to_translate.insert(dest);
	      }
	    else
	      {
		destroy(dest);
	      }
	  }
      }

    // Free all formulae.
    for (std::set<const formula*>::iterator i = formulae_seen.begin();
	 i != formulae_seen.end(); ++i)
      destroy(*i);
    for (succ_to_formula::iterator i = canonical_succ.begin();
     	 i != canonical_succ.end(); ++i)
      destroy(i->second);

    // Turn all promises into real acceptance conditions.
    a->complement_all_acceptance_conditions();
    return a;
  }

}