article

Conformant planning as a case study of incremental QBF solving

Authors:

Martin Kronegger,

Florian Lonsing,

Andreas PfandlerAuthors Info & Claims

Annals of Mathematics and Artificial Intelligence, Volume 80, Issue 1

Pages 21 - 45

https://doi.org/10.1007/s10472-016-9501-2

Published: 01 May 2017 Publication History

Abstract

We consider planning with uncertainty in the initial state as a case study of incremental quantified Boolean formula (QBF) solving. We report on experiments with a workflow to incrementally encode a planning instance into a sequence of QBFs. To solve this sequence of successively constructed QBFs, we use our general-purpose incremental QBF solver DepQBF. Since the generated QBFs have many clauses and variables in common, our approach avoids redundancy both in the encoding phase as well as in the solving phase. We also present experiments with incremental preprocessing techniques that are based on blocked clause elimination (QBCE). QBCE allows to eliminate certain clauses from a QBF in a satisfiability preserving way. We implemented the QBCE-based techniques in DepQBF in three variants: as preprocessing, as inprocessing (which extends preprocessing by taking into account variable assignments that were fixed by the QBF solver), and as a novel dynamic approach where QBCE is tightly integrated in the solving process. For DepQBF, experimental results show that incremental QBF solving with incremental QBCE outperforms incremental QBF solving without QBCE, which in turn outperforms nonincremental QBF solving. For the first time we report on incremental QBF solving with incremental QBCE as inprocessing. Our results are the first empirical study of incremental QBF solving in the context of planning and motivate its use in other application domains.

References

[1]

Audemard, G., Lagniez, J.M., Simon, L.: Improving Glucose for incremental SAT solving with assumptions: Application to MUS extraction. In: Proc. SAT 2013, LNCS, vol. 7962, pp. 309---317. Springer (2013)

Digital Library

[2]

Balabanov, V., Jiang, J.H.R.: Unified QBF certification and its applications. Formal Methods Syst. Des. 41(1), 45---65 (2012)

Digital Library

[3]

Baral, C., Kreinovich, V., Trejo, R.: Computational complexity of planning and approximate planning in the presence of incompleteness. Artif. Intell. 122(1-2), 241---267 (2000)

Digital Library

[4]

Beyersdorff, O., Chew, L., Janota, M.: Proof complexity of resolution-based QBF calculi. In: Proc. STACS 2015, LIPIcs, vol. 30, pp. 76---89. Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik (2015)

[5]

Biere, A.: Resolve and expand. In: Proc. SAT 2004, LNCS, vol. 3542, pp. 59---70. Springer (2004)

Digital Library

[6]

Biere, A., Lonsing, F., Seidl, M.: Blocked clause elimination for QBF. In: Proc. CADE 2011, LNCS, vol. 6803, pp. 101---115. Springer (2011)

Digital Library

[7]

Blum, A., Furst, M.L.: Fast planning through planning graph analysis. Artif. Intell. 90(1-2), 281---300 (1997)

Digital Library

[8]

Bubeck, U., Kleine Buning¿, H.: Bounded universal expansion for preprocessing QBF. In: Proc. SAT 2007, LNCS, vol. 4501, pp. 244---257. Springer (2007)

Digital Library

[9]

Cadoli, M., Schaerf, M., Giovanardi, A., Giovanardi, M.: An algorithm to evaluate quantified Boolean formulae and its experimental evaluation. J. Autom. Reas. 28(2), 101---142 (2002)

Digital Library

[10]

Cashmore, M., Fox, M., Giunchiglia, E.: Planning as quantified Boolean formula. In: Proc. ECAI, FAIA, vol. 242, pp. 217---222. IOS Press (2012)

Digital Library

[11]

Davis, M., Logemann, G., Loveland, D.: A machine program for theorem-proving. Commun. ACM 5(7), 394---397 (1962)

Digital Library

[12]

Eén, N., Sörensson, N.: Temporal induction by incremental SAT solving. Electron. Notes Theor. Comput. Sci. 89(4), 543---560 (2003)

[13]

Egly, U., Kronegger, M., Lonsing, F., Pfandler, A.: Conformant planning as a case study of incremental QBF solving. In: Proc. AISC 2014, LNCS, pp. 120---131. Springer (2014)

[14]

Giunchiglia, E., Marin, P.: Narizzano, M.: sQueezeBF: An effective preprocessor for QBFs based on equivalence reasoning. In: Proc. SAT 2010, LNCS, vol. 6175, pp. 85---98. Springer (2010)

Digital Library

[15]

Giunchiglia, E., Narizzano, M., Tacchella, A.: Clause/term resolution and learning in the evaluation of quantified Boolean formulas. J. Artif. Intell. Res. 26, 371---416 (2006)

[16]

Goultiaeva, A., Van Gelder, A., Bacchus, F.: A uniform approach for generating proofs and strategies for both true and false QBF formulas. In: Proc. IJCAI 2011, pp. 546---553. AAAI Press (2011)

Digital Library

[17]

Heule, M., Ja¿rvisalo, M., Lonsing, F., Seidl, M., Biere, A.: Clause elimination for SAT and QSAT. J. Artif. Intell. Res. 53, 127---168 (2015)

[18]

Heule, M., Seidl, M., Biere, A.: Efficient extraction of skolem functions from QRAT proofs. In: Proc. FMCAD 2014, pp. 107---114. IEEE (2014)

Digital Library

[19]

Heule, M., Seidl, M., Biere, A.: A unified proof system for QBF preprocessing. In: Proc. IJCAR 2014, LNCS, vol. 8562, pp. 91---106. Springer (2014)

[20]

Heyman, T., Smith, D., Mahajan, Y., Leong, L.: Abu-Haimed, H.: Dominant controllability check using QBF-solver and netlist optimizer. In: Proc. SAT 2014, LNCS, vol. 8561, pp. 227---242. Springer (2014)

[21]

Hoffmann, J., Brafman, R.I.: Conformant planning via heuristic forward search: A new approach. Artif. Intell 170(6---7), 507---541 (2006)

Digital Library

[22]

Janota, M., Grigore, R.: Marques-Silva, J.: On QBF proofs and preprocessing. In: Proc. LPAR 2013, LNCS, vol. 8312, pp. 473---489. Springer (2013)

[23]

Janota, M., Klieber, W., Marques-Silva, J., Clarke, E.M.: Solving QBF with counterexample guided refinement. In: Proc. SAT 2012, LNCS, vol. 7317, pp. 114---128. Springer (2012)

Digital Library

[24]

Janota, M., Marques-Silva, J.: Expansion-based QBF solving versus Q-resolution. Theor. Comput. Sci. 577, 25---42 (2015)

Digital Library

[25]

Ja¿rvisalo, M., Biere, A.: Reconstructing solutions after blocked clause elimination. In: Proc. SAT 2010, LNCS, vol. 6175, pp. 340---345. Springer (2010)

Digital Library

[26]

Ja¿rvisalo, M., Heule, M., Biere, A.: Inprocessing rules. In: Proc. IJCAR 2012, LNCS, vol. 7364, pp. 355---370. Springer (2012)

Digital Library

[27]

Kleine Büning, H., Karpinski, M., Flögel, A.: Resolution for quantified Boolean formulas. Inform. Comput. 117(1), 12---18 (1995)

Digital Library

[28]

Kronegger, M., Pfandler, A., Pichler, R.: Conformant planning as a benchmark for QBF-solvers. In: Proc. QBF 2013, pp. 1---5. http://fmv.jku.at/qbf2013/reportQBFWS13.pdf (2013)

[29]

Kullmann, O.: On a generalization of extended resolution. Discrete Appl. Math. 96---97, 149---176 (1999)

Digital Library

[30]

Lagniez, J.M., Biere, A.: Factoring out assumptions to speed up MUS extraction. In: Proc. SAT 2013, LNCS, vol. 7962, pp. 276---292. Springer (2013)

Digital Library

[31]

Letz, R.: Lemma and model caching in decision procedures for quantified Boolean formulas. In: Proc. TABLEAUX 2002, LNCS, vol. 2381, pp. 160---175. Springer (2002)

Digital Library

[32]

Lonsing, F., Bacchus, F., Biere, A., Egly, U., Seidl, M.: Enhancing search-based QBF solving by dynamic blocked clause elimination. In: Proc. LPAR 2015, LNCS, vol. 9450, pp. 418---433. Springer (2015)

Digital Library

[33]

Lonsing, F., Biere, A.: Nenofex: Expanding NNF for QBF solving. In: Proc. SAT 2008, LNCS, vol. 4996, pp. 196---210. Springer (2008)

Digital Library

[34]

Lonsing, F., Egly, U.: Incremental QBF solving. In: Proc. CP 2014, LNCS, vol. 8656, pp. 514---530. Springer (2014)

[35]

Lonsing, F., Egly, U.: Incremental QBF solving by DepQBF. In: Proc. ICMS 2014, LNCS, vol. 8592, pp. 307---314. Springer (2014)

[36]

Lonsing, F., Egly, U., Van Gelder, A.: Efficient clause learning for quantified Boolean formulas via QBF pseudo unit propagation. In: Proc. SAT 2013, LNCS, vol. 7962, pp. 100---115. Springer (2013)

Digital Library

[37]

Marin, P., Miller, C., Becker, B.: Incremental QBF preprocessing for partial design verification - (poster presentation). In: Proc. SAT 2012, LNCS, vol. 7317, pp. 473---474. Springer (2012)

Digital Library

[38]

Marin, P., Miller, C., Lewis, M.D.T., Becker, B.: Verification of partial designs using incremental QBF solving. In: Proc. DATE 2012, pp. 623---628. IEEE (2012)

Digital Library

[39]

Miller, C., Marin, P., Becker, B.: Verification of partial designs using incremental QBF. AI Commun. 28(2), 283---307 (2015)

Digital Library

[40]

Nadel, A., Ryvchin, V., Strichman, O.: Ultimately incremental SAT. In: Proc. SAT 2014, LNCS, vol. 8561, pp. 206---218. Springer (2014)

[41]

Niemetz, A., Preiner, M., Lonsing, F., Seidl, M., Biere, A.: Resolution-based certificate extraction for QBF - (tool presentation). In: Proc. SAT 2012, LNCS, vol. 7317, pp. 430---435. Springer (2012)

Digital Library

[42]

Palacios, H., Geffner, H.: Compiling uncertainty away in conformant planning problems with bounded width. J. Artif. Intell. Res. 35, 623---675 (2009)

[43]

Rintanen, J.: Asymptotically optimal encodings of conformant planning in QBF. In: Proc. AAAI 2007, pp. 1045---1050. AAAI Press (2007)

Digital Library

[44]

Samer, M., Szeider, S.: Backdoor sets of quantified Boolean formulas. J. Autom. Reas. 42(1), 77---97 (2009)

Digital Library

[45]

Samulowitz, H., Davies, J., Bacchus, F.: Preprocessing QBF. In: Proc. CP 2006, LNCS, vol. 4204, pp. 514---529. Springer (2006)

Digital Library

[46]

Seidl, M., Könighofer, R.: Partial witnesses from preprocessed quantified Boolean formulas. In: Proc. DATE 2014, pp. 1---6. IEEE (2014)

Digital Library

[47]

Smith, D.E., Weld, D.S.: Conformant graphplan. In: Proc. AAAI/IAAI 1998, pp. 889---896. AAAI Press / The MIT Press (1998)

Digital Library

[48]

Van Gelder, A., Wood, S.B., Lonsing, F.: Extended failed-literal preprocessing for quantified Boolean formulas. In: Proc. SAT 2012, LNCS, vol. 7317, pp. 86---99. Springer (2012)

Digital Library

[49]

Yu, Y., Malik, S.: Validating the result of a quantified Boolean formula (QBF) solver: theory and practice. In: Proc. ASP-DAC 2005, pp. 1047---1051. ACM Press (2005)

Digital Library

[50]

Zhang, L., Malik, S.: Towards a symmetric treatment of satisfaction and conflicts in quantified Boolean formula evaluation. In: Proc. CP 2002, LNCS, vol. 2470, pp. 200---215. Springer (2002)

Digital Library

Cited By

Beyersdorff OBlinkhorn JMahajan MPeitl T(2022)Hardness Characterisations and Size-width Lower Bounds for QBF ResolutionACM Transactions on Computational Logic10.1145/356528624:2(1-30)Online publication date: 28-Sep-2022
https://dl.acm.org/doi/10.1145/3565286
Beyersdorff OBlinkhorn JMahajan M(2021)Building Strategies into QBF ProofsJournal of Automated Reasoning10.1007/s10817-020-09560-165:1(125-154)Online publication date: 1-Jan-2021
https://dl.acm.org/doi/10.1007/s10817-020-09560-1
Bloem RBraud-Santoni NHadzic VEgly ULonsing FSeidl M(2021)Two SAT solvers for solving quantified Boolean formulas with an arbitrary number of quantifier alternationsFormal Methods in System Design10.1007/s10703-021-00371-757:2(157-177)Online publication date: 1-Aug-2021
https://dl.acm.org/doi/10.1007/s10703-021-00371-7
Show More Cited By

Recommendations

Asymptotically optimal encodings of conformant planning in QBF
AAAI'07: Proceedings of the 22nd national conference on Artificial intelligence - Volume 2

The world is unpredictable, and acting intelligently requires anticipating possible consequences of actions that are taken. Assuming that the actions and the world are deterministic, planning can be represented in the classical propositional logic. ...
Solving QBF with free variables
CP'13: Proceedings of the 19th International Conference on Principles and Practice of Constraint Programming

An open quantified boolean formula (QBF) is a QBF that contains free (unquantified) variables. A solution to such a QBF is a quantifier-free formula that is logically equivalent to the given QBF. Although most recent QBF research has focused on closed ...
Solving QBF with combined conjunctive and disjunctive normal form
AAAI'06: Proceedings of the 21st national conference on Artificial intelligence - Volume 1

Similar to most state-of-the-art Boolean Satisfiabilily (SAT) solvers, all contemporary Quantified Boolean Formula (QBF) solvers require inputs to be in the Conjunctive Normal Form (CNF). Most of them also store the QBF in CNF internally for reasoning. ...

Comments

Information & Contributors

Information

Published In

cover image Annals of Mathematics and Artificial Intelligence

Annals of Mathematics and Artificial Intelligence Volume 80, Issue 1

May 2017

110 pages

ISSN:1012-2443

Issue’s Table of Contents

Copyright © Copyright © 2017 Springer International Publishing Switzerland.

Publisher

Kluwer Academic Publishers

United States

Publication History

Published: 01 May 2017

Author Tags

Qualifiers

Article

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

11
Total Citations
View Citations
0
Total Downloads

Downloads (Last 12 months)0
Downloads (Last 6 weeks)0

Reflects downloads up to 16 Oct 2024

Other Metrics

View Author Metrics

Citations

Cited By

Beyersdorff OBlinkhorn JMahajan MPeitl T(2022)Hardness Characterisations and Size-width Lower Bounds for QBF ResolutionACM Transactions on Computational Logic10.1145/356528624:2(1-30)Online publication date: 28-Sep-2022
https://dl.acm.org/doi/10.1145/3565286
Beyersdorff OBlinkhorn JMahajan M(2021)Building Strategies into QBF ProofsJournal of Automated Reasoning10.1007/s10817-020-09560-165:1(125-154)Online publication date: 1-Jan-2021
https://dl.acm.org/doi/10.1007/s10817-020-09560-1
Bloem RBraud-Santoni NHadzic VEgly ULonsing FSeidl M(2021)Two SAT solvers for solving quantified Boolean formulas with an arbitrary number of quantifier alternationsFormal Methods in System Design10.1007/s10703-021-00371-757:2(157-177)Online publication date: 1-Aug-2021
https://dl.acm.org/doi/10.1007/s10703-021-00371-7
Beyersdorff OBonacina IChew LPich J(2020)Frege Systems for Quantified Boolean LogicJournal of the ACM10.1145/338188167:2(1-36)Online publication date: 5-Apr-2020
https://dl.acm.org/doi/10.1145/3381881
Beyersdorff OHinde LPich J(2020)Reasons for Hardness in QBF Proof SystemsACM Transactions on Computation Theory10.1145/337866512:2(1-27)Online publication date: 10-Feb-2020
https://dl.acm.org/doi/10.1145/3378665
Beyersdorff OBlinkhorn JMahajan MHermanns HZhang LKobayashi NMiller D(2020)Hardness Characterisations and Size-Width Lower Bounds for QBF ResolutionProceedings of the 35th Annual ACM/IEEE Symposium on Logic in Computer Science10.1145/3373718.3394793(209-223)Online publication date: 8-Jul-2020
https://dl.acm.org/doi/10.1145/3373718.3394793
Beyersdorff OBlinkhorn JPeitl TPulina LSeidl MChew LHeule MVallade VLe Frioux LBaarir SSopena JGanesh VKordon FFeng NBacchus FHickey RBacchus FMöhle SSebastiani RBiere AShaw AMeel KLorenz JWörz FAudemard GPaulevé LSimon LHeisinger MFleury MBiere ANabeshima HInoue KKochemazov SMull NPang SRazborov ABonet MLevy JVinyals MElffers JJohannsen JNordström JYolcu EWu XHeule MLarrosa JRollon ELi CFleming NVinyals MPitassi TGanesh VAgrawal DBhavishya Meel KSlivovsky FSzeider SBerg JBacchus FPoole AFilmus YMahajan MSood GVinyals Mde Colnet ALe Berre DMarquis PWallon RMencía CMarques-Silva JHecher MThier PWoltran SSeed TKing AEvans NJonáš MStrejček JBeyersdorff OBlinkhorn JPeitl TShukla ASlivovsky FSzeider SSchlaipfer MSlivovsky FWeissenbacher GZuleger FMayer-Eichberger VSaffidine AAnderson MJi ZXu AČeška MMatyáš JMrazek VVojnar TEhlers RTreutler KWesling VJanota MMorgado AKarpiński MPiotrów M(2020)Strong (D)QBF Dependency Schemes via Tautology-Free Resolution PathsTheory and Applications of Satisfiability Testing – SAT 202010.1007/978-3-030-51825-7_28(394-411)Online publication date: 3-Jul-2020
https://dl.acm.org/doi/10.1007/978-3-030-51825-7_28
Beyersdorff OBlinkhorn J(2019)Dynamic QBF Dependencies in Reduction and ExpansionACM Transactions on Computational Logic10.1145/335599521:2(1-27)Online publication date: 17-Nov-2019
https://dl.acm.org/doi/10.1145/3355995
Beyersdorff OChew LJanota M(2019)New Resolution-Based QBF Calculi and Their Proof ComplexityACM Transactions on Computation Theory10.1145/335215511:4(1-42)Online publication date: 12-Sep-2019
https://dl.acm.org/doi/10.1145/3352155
Blinkhorn JBeyersdorff O(2018)Dynamic dependency awareness for QBFProceedings of the 27th International Joint Conference on Artificial Intelligence10.5555/3304652.3304739(5224-5228)Online publication date: 13-Jul-2018
https://dl.acm.org/doi/10.5555/3304652.3304739
Show More Cited By

View Options

View options

Get Access

Login options

Check if you have access through your login credentials or your institution to get full access on this article.

Full Access

Get this Publication

Media

Figures

Other

Tables

View Issue’s Table of Contents