Adjust the WDBA test to count for sub-transitions.

* bench/wdba/run: Use -kt to count sub-transitions.
* bench/wdba/README: Adjust comments.

ChangeLog

+2011-02-08  Alexandre Duret-Lutz  <adl@lrde.epita.fr>
+
+	Adjust the WDBA test to count for sub-transitions.
+
+	* bench/wdba/run: Use -kt to count sub-transitions.
+	* bench/wdba/README: Adjust comments.
+
 2011-02-08  Alexandre Duret-Lutz  <adl@lrde.epita.fr>
 
 	Fix a spurious g++ warning observed on Darwin builds.

bench/wdba/README

@@ -28,58 +28,67 @@ Running the `./run' script should produce an output similar to the
 following:
 
 # form. nbr., states, trans., states minimized, trans. minimized, formula
-1, 2, 3, 2, 3, !(G(!p))
-2, 3, 5, 3, 5, !(Fr->(!p U r))
-3, 3, 6, 3, 6, !(G(q->G(!p)))
-4, 4, 8, 4, 9, !(G((q&!r&Fr)->(!p U r)))
-5, 3, 6, 3, 7, !(G(q&!r->((!p U r)|G!p)))
+1, 2, 4, 2, 4, !(G(!p))
+2, 3, 10, 3, 10, !(Fr->(!p U r))
+3, 3, 13, 3, 12, !(G(q->G(!p)))
+4, 4, 30, 4, 32, !(G((q&!r&Fr)->(!p U r)))
+5, 3, 21, 3, 24, !(G(q&!r->((!p U r)|G!p)))
 6, 1, 1, 1, 1, !(Fp)
-7, 2, 3, 2, 3, !((!r U (p&!r))|(G!r))
-8, 2, 3, 2, 3, !(G(!q)|F(q&Fp))
-9, 3, 5, 3, 6, !(G(q&!r->((!r U (p&!r))|G!r)))
-10, 6, 11, 6, 11, !((!p U ((p U ((!p U ((p U G!p)|Gp))|G!p))|Gp))|G!p)
-11, 7, 13, 7, 13, !(Fr->((!p&!r)U(r|((p&!r)U(r|((!p&!r)U(r|((p&!r)U(r|(!p U r))))))))))
-12, 7, 14, 7, 14, !(Fq->(!q U (q&((!p U ((p U ((!p U ((p U G!p)|Gp))|G!p))|Gp))|G!p))))
-13, 8, 16, 8, 21, !(G((q&Fr)->((!p&!r)U(r|((p&!r)U(r|((!p&!r)U(r|((p&!r)U(r|(!p U r)))))))))))
-14, 7, 14, 7, 19, !(G(q->((!p&!r)U(r|((p&!r)U(r|((!p&!r)U(r|((p&!r)U(r|((!p U r)|G!p)|Gp))))))))))
-15, 2, 3, 2, 3, !(G(p))
-16, 3, 5, 3, 5, !(Fr->(p U r))
-17, 3, 6, 3, 6, !(G(q->G(p)))
-18, 4, 7, 4, 8, !(G((p&!r&Fr)->(p U r)))
-19, 3, 6, 3, 7, !(G(q&!r->((p U r)|Gp)))
-20, 4, 7, 4, 7, !((!p U s)|Gp)
-21, 3, 5, 3, 5, !(Fr->(!p U (s|r)))
-22, 4, 8, 4, 9, !(G((q&!r&Fr)->(!p U (s|r))))
-23, 3, 6, 3, 7, !(G(q&!r->((!p U (s|r))|G!p)))
-24, 3, 5, 3, 6, !(Fr->(p->(!r U (s&!r))) U r)
-25, 4, 8, 4, 10, !(G((q&!r&Fr)->(p->(!r U (s&!r))) U r))
-26, 3, 6, 3, 6, !(Fp->(!p U (s&!p&X(!p U t))))
-27, 4, 8, 4, 8, !(Fr->(!p U (r|(s&!p&X(!p U t)))))
-28, 4, 9, 4, 9, !((G!q)|(!q U (q&Fp->(!p U (s&!p&X(!p U t))))))
-29, 5, 12, 5, 15, !(G((q&Fr)->(!p U (r|(s&!p&X(!p U t))))))
-30, 4, 10, 4, 13, !(G(q->(Fp->(!p U (r|(s&!p&X(!p U t)))))))
-31, 4, 8, 3, 5, !((F(s&XFt))->((!s) U p))
-32, 4, 7, 4, 7, !(Fr->((!(s&(!r)&X(!r U (t&!r))))U(r|p)))
-33, 5, 12, 4, 8, !((G!q)|((!q)U(q&((F(s&XFt))->((!s) U p)))))
-34, 5, 10, 5, 12, !(G((q&Fr)->((!(s&(!r)&X(!r U (t&!r))))U(r|p))))
-35, 10, 28, 4, 10, !(G(q->(!(s&(!r)&X(!r U (t&!r)))U(r|p)|G(!(s&XFt)))))
-36, 4, 8, 5, 18, !(Fr->(s&X(!r U t)->X(!r U (t&Fp))) U r)
-37, 4, 9, 4, 11, !(Fr->(p->(!r U (s&!r&X(!r U t)))) U r)
-38, 5, 13, 5, 17, !(G((q&Fr)->(p->(!r U (s&!r&X(!r U t)))) U r))
-39, 4, 10, 4, 11, !(Fr->(p->(!r U (s&!r&!z&X((!r&!z) U t)))) U r)
-40, 5, 14, 5, 17, !(G((q&Fr)->(p->(!r U (s&!r&!z&X((!r&!z) U t)))) U r))
+7, 2, 7, 2, 7, !((!r U (p&!r))|(G!r))
+8, 2, 5, 2, 5, !(G(!q)|F(q&Fp))
+9, 3, 23, 3, 24, !(G(q&!r->((!r U (p&!r))|G!r)))
+10, 6, 12, 6, 12, !((!p U ((p U ((!p U ((p U G!p)|Gp))|G!p))|Gp))|G!p)
+11, 7, 18, 7, 18, !(Fr->((!p&!r)U(r|((p&!r)U(r|((!p&!r)U(r|((p&!r)U(r|(!p U r))))))))))
+12, 7, 28, 7, 28, !(Fq->(!q U (q&((!p U ((p U ((!p U ((p U G!p)|Gp))|G!p))|Gp))|G!p))))
+13, 8, 46, 8, 64, !(G((q&Fr)->((!p&!r)U(r|((p&!r)U(r|((!p&!r)U(r|((p&!r)U(r|(!p U r)))))))))))
+14, 7, 38, 7, 56, !(G(q->((!p&!r)U(r|((p&!r)U(r|((!p&!r)U(r|((p&!r)U(r|((!p U r)|G!p)|Gp))))))))))
+15, 2, 4, 2, 4, !(G(p))
+16, 3, 10, 3, 10, !(Fr->(p U r))
+17, 3, 13, 3, 12, !(G(q->G(p)))
+18, 4, 15, 4, 16, !(G((p&!r&Fr)->(p U r)))
+19, 3, 21, 3, 24, !(G(q&!r->((p U r)|Gp)))
+20, 4, 12, 4, 12, !((!p U s)|Gp)
+21, 3, 18, 3, 18, !(Fr->(!p U (s|r)))
+22, 4, 54, 4, 64, !(G((q&!r&Fr)->(!p U (s|r))))
+23, 3, 37, 3, 48, !(G(q&!r->((!p U (s|r))|G!p)))
+24, 3, 19, 3, 20, !(Fr->(p->(!r U (s&!r))) U r)
+25, 4, 59, 4, 64, !(G((q&!r&Fr)->(p->(!r U (s&!r))) U r))
+26, 3, 20, 3, 20, !(Fp->(!p U (s&!p&X(!p U t))))
+27, 4, 44, 4, 44, !(Fr->(!p U (r|(s&!p&X(!p U t)))))
+28, 4, 48, 4, 48, !((G!q)|(!q U (q&Fp->(!p U (s&!p&X(!p U t))))))
+29, 5, 128, 5, 160, !(G((q&Fr)->(!p U (r|(s&!p&X(!p U t))))))
+30, 4, 92, 4, 128, !(G(q->(Fp->(!p U (r|(s&!p&X(!p U t)))))))
+31, 4, 34, 3, 20, !((F(s&XFt))->((!s) U p))
+32, 4, 46, 4, 44, !(Fr->((!(s&(!r)&X(!r U (t&!r))))U(r|p)))
+33, 5, 82, 4, 52, !((G!q)|((!q)U(q&((F(s&XFt))->((!s) U p)))))
+34, 5, 130, 5, 160, !(G((q&Fr)->((!(s&(!r)&X(!r U (t&!r))))U(r|p))))
+35, 10, 254, 4, 128, !(G(q->(!(s&(!r)&X(!r U (t&!r)))U(r|p)|G(!(s&XFt)))))
+36, 4, 36, 5, 50, !(Fr->(s&X(!r U t)->X(!r U (t&Fp))) U r)
+37, 4, 52, 4, 52, !(Fr->(p->(!r U (s&!r&X(!r U t)))) U r)
+38, 5, 148, 5, 160, !(G((q&Fr)->(p->(!r U (s&!r&X(!r U t)))) U r))
+39, 4, 104, 4, 104, !(Fr->(p->(!r U (s&!r&!z&X((!r&!z) U t)))) U r)
+40, 5, 296, 5, 320, !(G((q&Fr)->(p->(!r U (s&!r&!z&X((!r&!z) U t)))) U r))
 
 
 The first number is the number of the formula, so you can compare with
 the number displayed at http://www.daxc.de/eth/atva07/index.html.
-The second and third numbers give the number of states and transition
+The second and third numbers give the number of states and transitions
 of the automaton produced by Spot (with formula simplifications and SCC
 simplifications turned on), while the fourth and fifth number show the
 number of states and transitions with an additional WDBA minimization step.
 
+When counting transitions, we are actually counting the number of
+"sub-transitions".  That is, on an automaton defined over two atomic
+properties "p" and "q", a transition labelled by "p" actually stands
+for two sub-transitions labelled by "p&q" and "p&!q".  So we are
+counting it as two transitions.
+
 You can observe that some minimized automata have more transitions:
-this is because they have become deterministic.  There is even one
-case where the minimized automaton got one more state (formula 36).
+this is because their structure changed when they where determinized.
+Even though they have the same number of states as the non-minimized
+automaton, the states do not accept the same language.  There is even
+one case (formula 36) where the minimized automaton got one more
+state.
 
 In two cases (formulae 31 and 35) the minimization actually removed
 states in addition to making the automata deterministic.

bench/wdba/run

 #!/bin/sh
-# Copyright (C) 2010 Laboratoire de Recherche et Dveloppement
+# Copyright (C) 2010, 2011 Laboratoire de Recherche et Dveloppement
 # de l'Epita (LRDE).
 #
 # This file is part of Spot, a model checking library.
@@ -68,13 +68,13 @@ EOF
 line=0
 echo "# form. nbr., states, trans., states minimized, trans. minimized, formula"
 while read f; do
-  "$LTL2TGBA" -f -r7 -R3 -DS -k "!($f)" >out
+  "$LTL2TGBA" -f -r7 -x -R3 -DS -kt "!($f)" >out
   states=`sed -n 's/^states: \([0-9]*\)$/\1/p' out`
-  transitions=`sed -n 's/^transitions: \([0-9]*\)$/\1/p' out`
+  transitions=`sed -n 's/^sub trans.: \([0-9]*\)$/\1/p' out`
 
-  "$LTL2TGBA" -f -r1 -R3 -Rm -k "!($f)" >out
+  "$LTL2TGBA" -f -r1 -R3 -Rm -kt "!($f)" >out
   states2=`sed -n 's/^states: \([0-9]*\)$/\1/p' out`
-  transitions2=`sed -n 's/^transitions: \([0-9]*\)$/\1/p' out`
+  transitions2=`sed -n 's/^sub trans.: \([0-9]*\)$/\1/p' out`
 
   line=`expr $line + 1`
   echo "$line, $states, $transitions, $states2, $transitions2, !($f)"