simplify: GF(f)=GF(dnf(f)) FG(f)=FG(cnf(f))

These rules come from Delag's paper, and help some cases
in issue #385.

* spot/tl/simplify.cc: Implement the simplification.
* doc/tl/tl.tex, NEWS: Document it.
* tests/core/385.test: New file.
* tests/Makefile.am: Add it.
* tests/core/reduccmp.test: More tests.
* tests/core/ltl2tgba2.test: Adjust one improved case.
* tests/python/automata.ipynb, tests/python/twagraph-internals.ipynb:
Adjust expected output, as the cnf/dnf reorder some subformulas.

NEWS

@@ -105,9 +105,11 @@ New in spot 2.7.5.dev (not yet released)
 
   - The LTL simplifier learned the following optional rules:
     F(G(a | Fb)) = FGa | GFb  (if option "favor_event_univ")
-    G(F(a | Gb)) = GFa | FGb   (if option "favor_event_univ")
+    G(F(a | Gb)) = GFa | FGb  (if option "favor_event_univ")
     F(G(a & Fb) = FGa & GFb   (unless option "reduce_size_strictly")
     G(F(a & Gb)) = GFa & FGb  (unless option "reduce_size_strictly")
+    GF(f) = GF(dnf(f))        (unless option "reduce_size_strictly")
+    FG(f) = FG(cnf(f))        (unless option "reduce_size_strictly")
 
   - cleanup_parity() and colorize_parity() were cleaned up a bit,
     resulting in fewer colors used in some cases.  In particular,

doc/tl/tl.tex

@@ -116,7 +116,7 @@
 \newcommand{\nsereMarked}[1]{\texttt{!+\{}#1\texttt{\}}}
 \newcommand{\seren}[1]{\texttt{\{}#1\texttt{\}!}}
 
-% rewriting rules that enlarge the formula
+% rewriting rules that (may) enlarge the formula
 \newcommand{\equiV}{\stackrel{\star}{\equiv}}
 % rewriting rules that favors event/univ
 \newcommand{\equivEU}{\stackrel{\blacktriangleup}{\equiv}}
@@ -1463,15 +1463,19 @@ instead of $\equiv$, and they can be disabled by setting the
 \label{sec:basic-simp-ltl}
 
 The following are simplification rules for unary operators (applied
-from left to right, as usual):
+from left to right, as usual).  The terms $\mathsf{dnf}(f)$ and
+$\mathsf{cnf}(f)$ denote respectively the disjunctive and conjunctive
+normal forms if $f$, handling non-Boolean sub-formulas as if they were
+atomic propositions.
+
 \begin{align*}
-  \X\F\G f                                                    & \equiv \F\G f & \F(f\U g)        & \equiv \F g             & \G(f \R g)      & \equiv \G g             \\
-  \X\G\F f                                                    & \equiv \G\F f & \F(f\M g)        & \equiv \F (f\AND g)     & \G(f \W g)      & \equiv \G(f\OR g)       \\
-\F\X f                                                        & \equiv \X\F f & \F\G(f\AND \X g) & \equiv \F\G(f\AND g)    & \G\F(f\OR \X g) & \equiv \G\F(f\OR g)     \\
-\G\X f                                                        & \equiv \X\G f & \F\G(f\AND \G g) & \equiv \F\G(f\AND g)    & \G\F(f\OR \F g) & \equiv \G\F(f\OR g)     \\
-                                                              &               & \F\G(f\OR\G g)   & \equiv \F(\G f\OR\G g)  & \G\F(f\AND\F g) & \equiv \G(\F f\AND\F g) \\
-                                                              &               & \F\G(f\AND\F g)  & \equiV \F\G f\AND\G\F g & \G\F(f\AND\G g) & \equiV \G\F f\AND\F\G g \\
-                                                              &               & \F\G(f\OR\F g)  & \equivEU \F\G f\OR\G\F g & \G\F(f\OR\G g) & \equivEU \G\F f\OR\F\G g
+  \X\F\G f & \equiv \F\G f                & \F(f\U g)        & \equiv \F g              & \G(f \R g)      & \equiv \G g             \\
+  \X\G\F f & \equiv \G\F f                & \F(f\M g)        & \equiv \F (f\AND g)      & \G(f \W g)      & \equiv \G(f\OR g)       \\
+\F\X f     & \equiv \X\F f                & \F\G(f\AND \X g) & \equiv \F\G(f\AND g)     & \G\F(f\OR \X g) & \equiv \G\F(f\OR g)     \\
+\G\X f     & \equiv \X\G f                & \F\G(f\AND \G g) & \equiv \F\G(f\AND g)     & \G\F(f\OR \F g) & \equiv \G\F(f\OR g)     \\
+           &                              & \F\G(f\OR\G g)   & \equiv \F(\G f\OR\G g)   & \G\F(f\AND\F g) & \equiv \G(\F f\AND\F g) \\
+\G\F f     & \equiV \G\F(\mathsf{dnf}(f)) & \F\G(f\AND\F g)  & \equiV \F\G f\AND\G\F g  & \G\F(f\AND\G g) & \equiV \G\F f\AND\F\G g \\
+\F\G f     & \equiV \F\G(\mathsf{cnf}(f)) & \F\G(f\OR\F g)   & \equivEU \F\G f\OR\G\F g & \G\F(f\OR\G g)  & \equivEU \G\F f\OR\F\G g
 \end{align*}
 \begin{align*}
   \G(f_1\OR\ldots\OR f_n \OR \G\F(g_1)\OR\ldots\OR \G\F(g_m)) & \equiv \G(f_1\OR\ldots\OR f_n)\OR \G\F(g_1\OR\ldots\OR g_m)

spot/tl/simplify.cc

@@ -33,6 +33,7 @@
 #include <spot/tl/snf.hh>
 #include <spot/tl/length.hh>
 #include <spot/twa/formula2bdd.hh>
+#include <spot/misc/minato.hh>
 #include <cassert>
 #include <memory>
 
@@ -45,6 +46,7 @@ namespace spot
   {
     typedef std::unordered_map<formula, formula> f2f_map;
     typedef std::unordered_map<formula, bdd> f2b_map;
+    typedef std::map<int, formula> b2f_map;
     typedef std::pair<formula, formula> pairf;
     typedef std::map<pairf, bool> syntimpl_cache_t;
   public:
@@ -78,13 +80,18 @@ namespace spot
          << "syntactic implications: " << syntimpl_.size() << " entries\n"
          << "boolean to bdd:         " << as_bdd_.size() << " entries\n"
          << "star normal form:       " << snf_cache_.size() << " entries\n"
-         << "boolean isop:           " << bool_isop_.size() << " entries\n";
+         << "boolean isop:           " << bool_isop_.size() << " entries\n"
+         << "as dnf:                 " << as_dnf_.size() << " entries\n"
+         << "as cnf:                 " << as_cnf_.size() << " entries\n";
     }
 
     void
     clear_as_bdd_cache()
     {
       as_bdd_.clear();
+      for (auto p: bdd_to_f_)
+        dict->unregister_variable(p.first, this);
+      bdd_to_f_.clear();
     }
 
     // Convert a Boolean formula into a BDD for easier comparison.
@@ -136,7 +143,12 @@ namespace spot
             break;
           }
         default:
-          SPOT_UNIMPLEMENTED();
+          {
+            unsigned var = dict->register_anonymous_variables(1, this);
+            bdd_to_f_[var] = f;
+            result = bdd_ithvar(var);
+            break;
+          }
         }
 
       // Cache the result before returning.
@@ -144,6 +156,83 @@ namespace spot
       return result;
     }
 
+    formula as_xnf(formula f, bool cnf)
+    {
+      bdd in = as_bdd(f);
+      if (cnf)
+        in = !in;
+      minato_isop isop(in);
+      bdd cube;
+      vec clauses;
+      while ((cube = isop.next()) != bddfalse)
+        {
+          vec literals;
+          while (cube != bddtrue)
+            {
+              int var = bdd_var(cube);
+              const bdd_dict::bdd_info& i = dict->bdd_map[var];
+              formula res;
+              if (i.type == bdd_dict::var)
+                {
+                  res = i.f;
+                }
+              else
+                {
+                  res = bdd_to_f_[var];
+                  assert(res);
+                }
+              bdd high = bdd_high(cube);
+              if (high == bddfalse)
+                {
+                  if (!cnf)
+                    res = formula::Not(res);
+                  cube = bdd_low(cube);
+                }
+              else
+                {
+                  if (cnf)
+                    res = formula::Not(res);
+                  // If bdd_low is not false, then cube was not a
+                  // conjunction.
+                  assert(bdd_low(cube) == bddfalse);
+                  cube = high;
+                }
+              assert(cube != bddfalse);
+              literals.emplace_back(res);
+            }
+          if (cnf)
+            clauses.emplace_back(formula::Or(literals));
+          else
+            clauses.emplace_back(formula::And(literals));
+        }
+      if (cnf)
+        return formula::And(clauses);
+      else
+        return formula::Or(clauses);
+    }
+
+    formula as_dnf(formula f)
+    {
+      auto i = as_dnf_.find(f);
+      if (i != as_dnf_.end())
+        return i->second;
+      formula r = as_xnf(f, false);
+      as_dnf_[f] = r;
+      return r;
+    }
+
+    formula as_cnf(formula f)
+    {
+      auto i = as_cnf_.find(f);
+      if (i != as_cnf_.end())
+        return i->second;
+      formula r = as_xnf(f, true);
+      as_cnf_[f] = r;
+      return r;
+    }
+
+
+
     formula
     lookup_nenoform(formula f)
     {
@@ -303,7 +392,10 @@ namespace spot
 
   private:
     f2b_map as_bdd_;
+    b2f_map bdd_to_f_;
     f2f_map simplified_;
+    f2f_map as_dnf_;
+    f2f_map as_cnf_;
     f2f_map nenoform_;
     syntimpl_cache_t syntimpl_;
     snf_cache snf_cache_;
@@ -987,22 +1079,32 @@ namespace spot
                         return recurse(res);
                     }
 
-                  // FG(a & Xb) = FG(a & b)
-                  // FG(a & Gb) = FG(a & b)
-                  if (c.is({op::G, op::And}))
+                  // FG(a) = FG(dnf(a)) if a is not Boolean
+                  // and contains some | above non-Boolean subformulas.
+                  if (c.is(op::G) && !c[0].is_boolean())
                     {
                       formula m = c[0];
-                      if (!m.is_boolean())
-                        {
-                          formula out = m.map([](formula f)
-                                              {
-                                                if (f.is(op::X, op::G))
-                                                  return f[0];
-                                                return f;
-                                              });
-                          if (out != m)
-                            return recurse(unop_unop(op::F, op::G, out));
-                        }
+                      bool want_cnf = m.is(op::And);
+                      if (!want_cnf && m.is(op::Or))
+                        for (auto cc : m)
+                          if (cc.is(op::And))
+                            {
+                              want_cnf = true;
+                              break;
+                            }
+                      if (want_cnf && !opt_.reduce_size_strictly)
+                        m = c_->as_cnf(m);
+                      // FG(a & Xb) = FG(a & b)
+                      // FG(a & Gb) = FG(a & b)
+                      if (m.is(op::And))
+                        m = m.map([](formula f)
+                                  {
+                                    if (f.is(op::X, op::G))
+                                      return f[0];
+                                    return f;
+                                  });
+                      if (c[0] != m)
+                        return recurse(unop_unop(op::F, op::G, m));
                     }
                 }
               // if Fa => a, keep a.
@@ -1248,22 +1350,33 @@ namespace spot
                         return recurse(res);
                     }
 
-                  // GF(a | Xb) = GF(a | b)
-                  // GF(a | Fb) = GF(a | b)
-                  if (c.is({op::F, op::Or}))
+
+                  // GF(a) = GF(dnf(a)) if a is not Boolean
+                  // and contains some | above non-Boolean subformulas.
+                  if (c.is(op::F) && !c[0].is_boolean())
                     {
                       formula m = c[0];
-                      if (!m.is_boolean())
-                        {
-                          formula out = m.map([](formula f)
-                                              {
-                                                if (f.is(op::X, op::F))
-                                                  return f[0];
-                                                return f;
-                                              });
-                          if (out != m)
-                            return recurse(unop_unop(op::G, op::F, out));
-                        }
+                      bool want_dnf = m.is(op::Or);
+                      if (!want_dnf && m.is(op::And))
+                        for (auto cc : m)
+                          if (cc.is(op::Or))
+                            {
+                              want_dnf = true;
+                              break;
+                            }
+                      if (want_dnf && !opt_.reduce_size_strictly)
+                        m = c_->as_dnf(m);
+                      // GF(a | Xb) = GF(a | b)
+                      // GF(a | Fb) = GF(a | b)
+                      if (m.is(op::Or))
+                        m = m.map([](formula f)
+                                  {
+                                    if (f.is(op::X, op::F))
+                                      return f[0];
+                                    return f;
+                                  });
+                      if (c[0] != m)
+                        return recurse(unop_unop(op::G, op::F, m));
                     }
                   // GF(f1 & f2 & eu1 & eu2) = G(F(f1 & f2) & eu1 & eu2
                   if (opt_.event_univ && c.is({op::F, op::And}))

tests/Makefile.am

@@ -208,6 +208,7 @@ TESTS_misc = \
   core/trival.test
 
 TESTS_twa = \
+  core/385.test \
   core/acc.test \
   core/acc2.test \
   core/bdddict.test \

tests/core/385.test

+#!/bin/sh
+# -*- coding: utf-8 -*-
+# Copyright (C) 2019 Laboratoire de Recherche et Développement 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 3 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 this program.  If not, see <http://www.gnu.org/licenses/>.
+
+. ./defs
+
+set -e
+
+# Formulas from issue #385.
+
+ltl2tgba -G --stats=%s,%f> out <<EOF
+GFX((e & XXXa) -> (e & X!d))
+G(Gc | Fa | F!G(c | Ge))
+Ge | XGF(Ge & X(c & Fd))
+G!GXXe -> GF(b & c & Gc)
+G!(Gd & (c | Fb))
+XF(F(Gc & Xb) -> a)
+EOF
+
+# Some of the following are still not optimal.
+cat >expected <<EOF
+1,GF(!a | !d | !e)
+6,G(Gc | F(a | (!c & F!e)))
+2,Ge | G(Fd & FGe & Fc)
+1,F(G(Fb & FGc) | Ge)
+4,G(F!d | (!c & G!b))
+3,F(GF!c | G!b) | XFa
+EOF
+diff out expected

tests/core/ltl2tgba2.test

@@ -369,7 +369,7 @@ diff output expected
 cat >formulas <<EOF
 GF((a & XXa) | (!a & XX!a)), 4,8, 4,8, 6,14, 7,14, 4,8
 GF((a & XXXa) | (!a & XXX!a)), 7,14, 8,16, 8,18, 15,30, 8,16
-GF(((a & Xb) | XXc) & Xd), 4,64, 4,64, 5,80, 5,80, 4,64
+GF(((a & Xb) | XXc) & Xd), 3,58, 4,64, 3,58, 5,80, 4,64
 GF((b | Fa) & (b R Xb)), 2,4, 2,4, 3,6, 3,12, 2,4
 G(F(a & Xa) & F(a & X!a)), 2,4, 2,4, 4,8, 4,8, 3,6
 G(!p0 & F(p1 & XG!p1)), 1,0, 1,0, 1,0, 1,0, 1,0

tests/core/reduccmp.test

@@ -346,6 +346,8 @@ F(G(a & Fb)), G(Fb & FGa)
 G(F(a & Gb)), G(Fa & FGb)
 Ge | XGF(Ge & X(c & Fd)), Ge | G(Fd & FGe & Fc)
 G!GXXe -> GF(b & c & Gc), F(G(Fb & FGc) | Ge)
+GFX((e & XXXa) -> (e & X!d)), GF(!a | !d | !e)
+!GFX((e & XXXa) -> (e & X!d)), FG(a & d & e)
 
 # Because reduccmp will translate the formula,
 # this also check for an old bug in ltl2tgba_fm.