Skip to main content

2017 | OriginalPaper | Buchkapitel

HQSpre – An Effective Preprocessor for QBF and DQBF

verfasst von : Ralf Wimmer, Sven Reimer, Paolo Marin, Bernd Becker

Erschienen in: Tools and Algorithms for the Construction and Analysis of Systems

Verlag: Springer Berlin Heidelberg

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

We present our new preprocessor HQSpre, a state-of-the-art tool for simplifying quantified Boolean formulas (QBFs) and the first available preprocessor for dependency quantified Boolean formulas (DQBFs). The latter are a generalization of QBFs, resulting from adding so-called Henkin-quantifiers to QBFs. HQSpre applies most of the preprocessing techniques that have been proposed in the literature. It can be used both as a standalone tool and as a library. It is possible to tailor it towards different solver back-ends, e. g., to preserve the circuit structure of the formula when a non-CNF solver back-end is used. Extensive experiments show that HQSpre allows QBF solvers to solve more benchmark instances and is able to decide more instances on its own than state-of-the-art tools. The same impact can be observed in the DQBF domain as well.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Fußnoten
1
The syntactic constant detection using transitive implication chains is not included.
 
2
Note, this covers also OR gates with arbitrarily negated inputs and output.
 
3
A job consists of preprocessing and, where applicable, solving one formula. To guarantee repeatability, the sub-job of preprocessing a formula was performed once for all the solvers.
 
Literatur
1.
Zurück zum Zitat Balabanov, V., Chiang, H.K., Jiang, J.R.: Henkin quantifiers and Boolean formulae: a certification perspective of DQBF. Theoret. Comput. Sci. 523, 86–100 (2014)MathSciNetCrossRefMATH Balabanov, V., Chiang, H.K., Jiang, J.R.: Henkin quantifiers and Boolean formulae: a certification perspective of DQBF. Theoret. Comput. Sci. 523, 86–100 (2014)MathSciNetCrossRefMATH
4.
Zurück zum Zitat Biere, A., Cimatti, A., Clarke, E.M., Strichman, O., Zhu, Y.: Bounded model checking. Adv. Comput. 58, 117–148 (2003)CrossRef Biere, A., Cimatti, A., Clarke, E.M., Strichman, O., Zhu, Y.: Bounded model checking. Adv. Comput. 58, 117–148 (2003)CrossRef
5.
Zurück zum Zitat Biere, A., Heule, M., van Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. Frontiers in Artificial Intelligence and Applications, vol. 185. IOS Press, Amsterdam (2008) Biere, A., Heule, M., van Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. Frontiers in Artificial Intelligence and Applications, vol. 185. IOS Press, Amsterdam (2008)
6.
Zurück zum Zitat Biere, A., Lonsing, F., Seidl, M.: Blocked clause elimination for QBF. In: Bjørner, N., Sofronie-Stokkermans, V. (eds.) CADE 2011. LNCS (LNAI), vol. 6803, pp. 101–115. Springer, Heidelberg (2011). doi:10.1007/978-3-642-22438-6_10 CrossRef Biere, A., Lonsing, F., Seidl, M.: Blocked clause elimination for QBF. In: Bjørner, N., Sofronie-Stokkermans, V. (eds.) CADE 2011. LNCS (LNAI), vol. 6803, pp. 101–115. Springer, Heidelberg (2011). doi:10.​1007/​978-3-642-22438-6_​10 CrossRef
7.
Zurück zum Zitat Bloem, R., Könighofer, R., Seidl, M.: SAT-based synthesis methods for safety specs. In: McMillan, K.L., Rival, X. (eds.) VMCAI 2014. LNCS, vol. 8318, pp. 1–20. Springer, Heidelberg (2014). doi:10.1007/978-3-642-54013-4_1 CrossRef Bloem, R., Könighofer, R., Seidl, M.: SAT-based synthesis methods for safety specs. In: McMillan, K.L., Rival, X. (eds.) VMCAI 2014. LNCS, vol. 8318, pp. 1–20. Springer, Heidelberg (2014). doi:10.​1007/​978-3-642-54013-4_​1 CrossRef
8.
Zurück zum Zitat Bubeck, U., Kleine Büning, H.: Bounded universal expansion for preprocessing QBF. In: Marques-Silva, J., Sakallah, K.A. (eds.) SAT 2007. LNCS, vol. 4501, pp. 244–257. Springer, Heidelberg (2007). doi:10.1007/978-3-540-72788-0_24 CrossRef Bubeck, U., Kleine Büning, H.: Bounded universal expansion for preprocessing QBF. In: Marques-Silva, J., Sakallah, K.A. (eds.) SAT 2007. LNCS, vol. 4501, pp. 244–257. Springer, Heidelberg (2007). doi:10.​1007/​978-3-540-72788-0_​24 CrossRef
9.
Zurück zum Zitat del Val, A.: Simplifying binary propositional theories into connected components twice as fast. In: Nieuwenhuis, R., Voronkov, A. (eds.) LPAR 2001. LNCS (LNAI), vol. 2250, pp. 392–406. Springer, Heidelberg (2001). doi:10.1007/3-540-45653-8_27 CrossRef del Val, A.: Simplifying binary propositional theories into connected components twice as fast. In: Nieuwenhuis, R., Voronkov, A. (eds.) LPAR 2001. LNCS (LNAI), vol. 2250, pp. 392–406. Springer, Heidelberg (2001). doi:10.​1007/​3-540-45653-8_​27 CrossRef
10.
Zurück zum Zitat Eén, N., Biere, A.: Effective preprocessing in SAT through variable and clause elimination. In: Bacchus, F., Walsh, T. (eds.) SAT 2005. LNCS, vol. 3569, pp. 61–75. Springer, Heidelberg (2005). doi:10.1007/11499107_5 CrossRef Eén, N., Biere, A.: Effective preprocessing in SAT through variable and clause elimination. In: Bacchus, F., Walsh, T. (eds.) SAT 2005. LNCS, vol. 3569, pp. 61–75. Springer, Heidelberg (2005). doi:10.​1007/​11499107_​5 CrossRef
11.
Zurück zum Zitat Eggersglüß, S., Drechsler, R.: A highly fault-efficient SAT-based ATPG flow. IEEE Des. Test Comput. 29(4), 63–70 (2012)CrossRef Eggersglüß, S., Drechsler, R.: A highly fault-efficient SAT-based ATPG flow. IEEE Des. Test Comput. 29(4), 63–70 (2012)CrossRef
13.
Zurück zum Zitat Fröhlich, A., Kovásznai, G., Biere, A., Veith, H.: iDQ: instantiation-based DQBF solving. In: Le Berre, D. (ed.) International Workshop on Pragmatics of SAT (POS). EPiC Series, vol. 27, pp. 103–116. EasyChair (2014) Fröhlich, A., Kovásznai, G., Biere, A., Veith, H.: iDQ: instantiation-based DQBF solving. In: Le Berre, D. (ed.) International Workshop on Pragmatics of SAT (POS). EPiC Series, vol. 27, pp. 103–116. EasyChair (2014)
14.
Zurück zum Zitat Gitina, K., Reimer, S., Sauer, M., Wimmer, R., Scholl, C., Becker, B.: Equivalence checking of partial designs using dependency quantified Boolean formulae. In: Proceedings of ICCD, pp. 396–403. IEEE CS (2013) Gitina, K., Reimer, S., Sauer, M., Wimmer, R., Scholl, C., Becker, B.: Equivalence checking of partial designs using dependency quantified Boolean formulae. In: Proceedings of ICCD, pp. 396–403. IEEE CS (2013)
15.
Zurück zum Zitat Gitina, K., Wimmer, R., Reimer, S., Sauer, M., Scholl, C., Becker, B.: Solving DQBF through quantifier elimination. In: Proceedings of DATE, pp. 1617–1622. IEEE (2015) Gitina, K., Wimmer, R., Reimer, S., Sauer, M., Scholl, C., Becker, B.: Solving DQBF through quantifier elimination. In: Proceedings of DATE, pp. 1617–1622. IEEE (2015)
16.
Zurück zum Zitat Giunchiglia, E., Marin, P., Narizzano, M.: QuBE7.0. J. Satisf. Boolean Model. Comput. 7(2–3), 83–88 (2010) Giunchiglia, E., Marin, P., Narizzano, M.: QuBE7.0. J. Satisf. Boolean Model. Comput. 7(2–3), 83–88 (2010)
17.
Zurück zum Zitat Giunchiglia, E., Marin, P., Narizzano, M.: sQueezeBF: an effective preprocessor for QBFs based on equivalence reasoning. In: Strichman, O., Szeider, S. (eds.) SAT 2010. LNCS, vol. 6175, pp. 85–98. Springer, Heidelberg (2010). doi:10.1007/978-3-642-14186-7_9 CrossRef Giunchiglia, E., Marin, P., Narizzano, M.: sQueezeBF: an effective preprocessor for QBFs based on equivalence reasoning. In: Strichman, O., Szeider, S. (eds.) SAT 2010. LNCS, vol. 6175, pp. 85–98. Springer, Heidelberg (2010). doi:10.​1007/​978-3-642-14186-7_​9 CrossRef
18.
Zurück zum Zitat Heule, M., Järvisalo, M., Lonsing, F., Seidl, M., Biere, A.: Clause elimination for SAT and QSAT. J. Artif. Intell. Res. 53, 127–168 (2015)MathSciNetMATH Heule, M., Järvisalo, M., Lonsing, F., Seidl, M., Biere, A.: Clause elimination for SAT and QSAT. J. Artif. Intell. Res. 53, 127–168 (2015)MathSciNetMATH
19.
Zurück zum Zitat Janota, M., Klieber, W., Marques-Silva, J., Clarke, E.: Solving QBF with counterexample guided refinement. In: Cimatti, A., Sebastiani, R. (eds.) SAT 2012. LNCS, vol. 7317, pp. 114–128. Springer, Heidelberg (2012). doi:10.1007/978-3-642-31612-8_10 CrossRef Janota, M., Klieber, W., Marques-Silva, J., Clarke, E.: Solving QBF with counterexample guided refinement. In: Cimatti, A., Sebastiani, R. (eds.) SAT 2012. LNCS, vol. 7317, pp. 114–128. Springer, Heidelberg (2012). doi:10.​1007/​978-3-642-31612-8_​10 CrossRef
20.
Zurück zum Zitat Janota, M., Marques-Silva, J.: Solving QBF by clause selection. In: Proceedings of IJCAI, pp. 325–331. AAAI Press (2015) Janota, M., Marques-Silva, J.: Solving QBF by clause selection. In: Proceedings of IJCAI, pp. 325–331. AAAI Press (2015)
22.
Zurück zum Zitat Klieber, W., Sapra, S., Gao, S., Clarke, E.: A non-prenex, non-clausal QBF solver with game-state learning. In: Strichman, O., Szeider, S. (eds.) SAT 2010. LNCS, vol. 6175, pp. 128–142. Springer, Heidelberg (2010). doi:10.1007/978-3-642-14186-7_12 CrossRef Klieber, W., Sapra, S., Gao, S., Clarke, E.: A non-prenex, non-clausal QBF solver with game-state learning. In: Strichman, O., Szeider, S. (eds.) SAT 2010. LNCS, vol. 6175, pp. 128–142. Springer, Heidelberg (2010). doi:10.​1007/​978-3-642-14186-7_​12 CrossRef
23.
Zurück zum Zitat Kupferschmid, S., Lewis, M., Schubert, T., Becker, B.: Incremental preprocessing methods for use in BMC. Form. Methods Syst. Des. 39(2), 185–204 (2011)CrossRefMATH Kupferschmid, S., Lewis, M., Schubert, T., Becker, B.: Incremental preprocessing methods for use in BMC. Form. Methods Syst. Des. 39(2), 185–204 (2011)CrossRefMATH
24.
Zurück zum Zitat Li, C.M., Anbulagan, A.: Heuristics based on unit propagation for satisfiability problems. In: Proceedings of IJCAI, vol. 1, pp. 366–371. Morgan Kaufmann Publishers Inc. (1997) Li, C.M., Anbulagan, A.: Heuristics based on unit propagation for satisfiability problems. In: Proceedings of IJCAI, vol. 1, pp. 366–371. Morgan Kaufmann Publishers Inc. (1997)
25.
Zurück zum Zitat Lonsing, F., Bacchus, F., Biere, A., Egly, U., Seidl, M.: Enhancing search-based QBF solving by dynamic blocked clause elimination. In: Davis, M., Fehnker, A., McIver, A., Voronkov, A. (eds.) LPAR 2015. LNCS, vol. 9450, pp. 418–433. Springer, Heidelberg (2015). doi:10.1007/978-3-662-48899-7_29 CrossRef Lonsing, F., Bacchus, F., Biere, A., Egly, U., Seidl, M.: Enhancing search-based QBF solving by dynamic blocked clause elimination. In: Davis, M., Fehnker, A., McIver, A., Voronkov, A. (eds.) LPAR 2015. LNCS, vol. 9450, pp. 418–433. Springer, Heidelberg (2015). doi:10.​1007/​978-3-662-48899-7_​29 CrossRef
26.
Zurück zum Zitat Meyer, A.R., Stockmeyer, L.J.: Word problems requiring exponential time: preliminary report. In: Proceedings of STOC, pp. 1–9. ACM Press (1973) Meyer, A.R., Stockmeyer, L.J.: Word problems requiring exponential time: preliminary report. In: Proceedings of STOC, pp. 1–9. ACM Press (1973)
27.
Zurück zum Zitat Peterson, G., Reif, J., Azhar, S.: Lower bounds for multiplayer non-cooperative games of incomplete information. Comput. Math. Appl. 41(7–8), 957–992 (2001)MathSciNetCrossRefMATH Peterson, G., Reif, J., Azhar, S.: Lower bounds for multiplayer non-cooperative games of incomplete information. Comput. Math. Appl. 41(7–8), 957–992 (2001)MathSciNetCrossRefMATH
28.
Zurück zum Zitat Piette, C., Hamadi, Y., Sais, L.: Vivifying propositional clausal formulae. In: Ghallab, M., Spyropoulos, C.D., Fakotakis, N., Avouris, N.M. (eds.) Proceedings of ECAI. Frontiers in Artificial Intelligence and Applications, vol. 178, pp. 525–529. IOS Press (2008) Piette, C., Hamadi, Y., Sais, L.: Vivifying propositional clausal formulae. In: Ghallab, M., Spyropoulos, C.D., Fakotakis, N., Avouris, N.M. (eds.) Proceedings of ECAI. Frontiers in Artificial Intelligence and Applications, vol. 178, pp. 525–529. IOS Press (2008)
29.
Zurück zum Zitat Pigorsch, F., Scholl, C.: Exploiting structure in an AIG based QBF solver. In: Proceedings of DATE, pp. 1596–1601. IEEE (2009) Pigorsch, F., Scholl, C.: Exploiting structure in an AIG based QBF solver. In: Proceedings of DATE, pp. 1596–1601. IEEE (2009)
30.
Zurück zum Zitat Pigorsch, F., Scholl, C.: An AIG-based QBF-solver using SAT for preprocessing. In: Sapatnekar, S.S. (ed.) Proceedings of DAC, pp. 170–175. ACM Press (2010) Pigorsch, F., Scholl, C.: An AIG-based QBF-solver using SAT for preprocessing. In: Sapatnekar, S.S. (ed.) Proceedings of DAC, pp. 170–175. ACM Press (2010)
31.
33.
Zurück zum Zitat Rintanen, J., Heljanko, K., Niemelä, I.: Planning as satisfiability: parallel plans and algorithms for plan search. Artif. Intell. 170(12–13), 1031–1080 (2006)MathSciNetCrossRefMATH Rintanen, J., Heljanko, K., Niemelä, I.: Planning as satisfiability: parallel plans and algorithms for plan search. Artif. Intell. 170(12–13), 1031–1080 (2006)MathSciNetCrossRefMATH
35.
Zurück zum Zitat Scholl, C., Becker, B.: Checking equivalence for partial implementations. In: Proceedings of DAC, pp. 238–243. ACM Press (2001) Scholl, C., Becker, B.: Checking equivalence for partial implementations. In: Proceedings of DAC, pp. 238–243. ACM Press (2001)
37.
38.
Zurück zum Zitat Tentrup, L., Rabe, M.N.: CAQE: a certifying QBF solver. In: Proceedings of FMCAD, pp. 136–143. IEEE (2015) Tentrup, L., Rabe, M.N.: CAQE: a certifying QBF solver. In: Proceedings of FMCAD, pp. 136–143. IEEE (2015)
39.
Zurück zum Zitat Tseitin, G.S.: On the complexity of derivation in propositional calculus. Stud. Constr. Math. Math. Log. Part 2, 115–125 (1970)CrossRef Tseitin, G.S.: On the complexity of derivation in propositional calculus. Stud. Constr. Math. Math. Log. Part 2, 115–125 (1970)CrossRef
41.
Zurück zum Zitat Wimmer, R., Scholl, C., Wimmer, K., Becker, B.: Dependency schemes for DQBF. In: Creignou, N., Le Berre, D. (eds.) SAT 2016. LNCS, vol. 9710, pp. 473–489. Springer, Cham (2016). doi:10.1007/978-3-319-40970-2_29 Wimmer, R., Scholl, C., Wimmer, K., Becker, B.: Dependency schemes for DQBF. In: Creignou, N., Le Berre, D. (eds.) SAT 2016. LNCS, vol. 9710, pp. 473–489. Springer, Cham (2016). doi:10.​1007/​978-3-319-40970-2_​29
Metadaten
Titel
HQSpre – An Effective Preprocessor for QBF and DQBF
verfasst von
Ralf Wimmer
Sven Reimer
Paolo Marin
Bernd Becker
Copyright-Jahr
2017
Verlag
Springer Berlin Heidelberg
DOI
https://doi.org/10.1007/978-3-662-54577-5_21