edc71b807e
* bench/wdba/: New directory. * bench/Makefile.am (SUBDIRS): Add wdba. * NEWS: Mention it. * configure.ac: Output bench/wdba/defs and bench/wdba/Makefile.
85 lines
3.9 KiB
Text
85 lines
3.9 KiB
Text
This benchmark shows the size of 40 obligation formulae translated by
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Spot to degeneralized state-based Büchi automata, before and after
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reductions using the WDBA technique introduced in the following paper.
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@InProceedings{ dax.07.atva,
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author = {Christian Dax and Jochen Eisinger and Felix Klaedtke},
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title = {Mechanizing the Powerset Construction for Restricted
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Classes of {$\omega$}-Automata},
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year = 2007,
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series = {Lecture Notes in Computer Science},
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publisher = {Springer-Verlag},
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volume = 4762,
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booktitle = {Proceedings of the 5th International Symposium on
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Automated Technology for Verification and Analysis
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(ATVA'07)},
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editor = {Kedar S. Namjoshi and Tomohiro Yoneda and Teruo Higashino
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and Yoshio Okamura},
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month = oct
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}
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This is meant to complement the experiment 1 at
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http://www.daxc.de/eth/atva07/index.html
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The formulae used here are the same as the formulae used on the above
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page, and are presented in the same order.
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Running the `./run' script should produce an output similar to the
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following:
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# form. nbr., states, trans., states minimized, trans. minimized, formula
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1, 2, 3, 2, 3, !(G(!p))
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2, 3, 5, 3, 5, !(Fr->(!p U r))
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3, 3, 6, 3, 6, !(G(q->G(!p)))
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4, 4, 8, 4, 9, !(G((q&!r&Fr)->(!p U r)))
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5, 3, 6, 3, 7, !(G(q&!r->((!p U r)|G!p)))
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6, 1, 1, 1, 1, !(Fp)
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7, 2, 3, 2, 3, !((!r U (p&!r))|(G!r))
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8, 2, 3, 2, 3, !(G(!q)|F(q&Fp))
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9, 3, 5, 3, 6, !(G(q&!r->((!r U (p&!r))|G!r)))
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10, 6, 11, 6, 11, !((!p U ((p U ((!p U ((p U G!p)|Gp))|G!p))|Gp))|G!p)
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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))))))))))
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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))))
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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)))))))))))
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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))))))))))
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15, 2, 3, 2, 3, !(G(p))
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16, 3, 5, 3, 5, !(Fr->(p U r))
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17, 3, 6, 3, 6, !(G(q->G(p)))
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18, 4, 7, 4, 8, !(G((p&!r&Fr)->(p U r)))
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19, 3, 6, 3, 7, !(G(q&!r->((p U r)|Gp)))
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20, 4, 7, 4, 7, !((!p U s)|Gp)
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21, 3, 5, 3, 5, !(Fr->(!p U (s|r)))
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22, 4, 8, 4, 9, !(G((q&!r&Fr)->(!p U (s|r))))
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23, 3, 6, 3, 7, !(G(q&!r->((!p U (s|r))|G!p)))
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24, 3, 5, 3, 6, !(Fr->(p->(!r U (s&!r))) U r)
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25, 4, 8, 4, 10, !(G((q&!r&Fr)->(p->(!r U (s&!r))) U r))
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26, 3, 6, 3, 6, !(Fp->(!p U (s&!p&X(!p U t))))
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27, 4, 8, 4, 8, !(Fr->(!p U (r|(s&!p&X(!p U t)))))
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28, 4, 9, 4, 9, !((G!q)|(!q U (q&Fp->(!p U (s&!p&X(!p U t))))))
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29, 5, 12, 5, 15, !(G((q&Fr)->(!p U (r|(s&!p&X(!p U t))))))
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30, 4, 10, 4, 13, !(G(q->(Fp->(!p U (r|(s&!p&X(!p U t)))))))
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31, 4, 8, 3, 5, !((F(s&XFt))->((!s) U p))
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32, 4, 7, 4, 7, !(Fr->((!(s&(!r)&X(!r U (t&!r))))U(r|p)))
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33, 5, 12, 4, 8, !((G!q)|((!q)U(q&((F(s&XFt))->((!s) U p)))))
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34, 5, 10, 5, 12, !(G((q&Fr)->((!(s&(!r)&X(!r U (t&!r))))U(r|p))))
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35, 10, 28, 4, 10, !(G(q->(!(s&(!r)&X(!r U (t&!r)))U(r|p)|G(!(s&XFt)))))
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36, 4, 8, 5, 18, !(Fr->(s&X(!r U t)->X(!r U (t&Fp))) U r)
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37, 4, 9, 4, 11, !(Fr->(p->(!r U (s&!r&X(!r U t)))) U r)
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38, 5, 13, 5, 17, !(G((q&Fr)->(p->(!r U (s&!r&X(!r U t)))) U r))
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39, 4, 10, 4, 11, !(Fr->(p->(!r U (s&!r&!z&X((!r&!z) U t)))) U r)
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40, 5, 14, 5, 17, !(G((q&Fr)->(p->(!r U (s&!r&!z&X((!r&!z) U t)))) U r))
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The first number is the number of the formula, so you can compare with
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the number displayed at http://www.daxc.de/eth/atva07/index.html.
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The second and third numbers give the number of states and transition
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of the automaton produced by Spot (with formula simplifications and SCC
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simplifications turned on), while the fourth and fifth number show the
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number of states and transitions with an additional WDBA minimization step.
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You can observe that some minimized automata have more transitions:
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this is because they have become deterministic. There is even one
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case where the minimized automaton got one more state (formula 36).
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In two cases (formulae 31 and 35) the minimization actually removed
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states in addition to making the automata deterministic.
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