Incremental QBF Solving

Lonsing, Florian; Egly, Uwe

doi:10.1007/978-3-319-10428-7_38

Cited by 16 publications

(16 citation statements)

References 35 publications

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“…Also, additional complexity in the structure of the encodings due to the Tseitin transformation that is required to transform the encodings to the prenex conjunctive normal form (PCNF) required by most QSAT solvers may be avoided by using a QSAT solver that does not require the input to be in PCNF. Finally we plan to investigate algorithms using recent advances in incremental QBF solving (Lonsing & Egly, 2014). Incremental algorithms can, for example, compute a preferred interpretation by incrementally computing admissible interpretations with increasing information until an information maximal interpretation is found.…”

Section: Resultsmentioning

confidence: 99%

Reasoning in abstract dialectical frameworks using quantified Boolean formulas

Diller¹,

Wallner²,

Woltran³

2015

Argument & Computation

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dialectical frameworks (ADFs) constitute a recent and powerful generalisation of Dung's argumentation frameworks (AFs), where the relationship between the arguments can be specified via Boolean formulas. Recent results have shown that this enhancement comes with the price of higher complexity compared to AFs. In fact, acceptance problems in the world of ADFs can be hard even for the third level of the polynomial hierarchy. In order to implement reasoning problems on ADFs, systems for quantified Boolean formulas (QBFs) thus are suitable engines to be employed. In this paper we give complexity sensitive QBF encodings of ADF problems generalising recent work on QBFs for AF labellings. Our encodings provide a uniform and modular way of translating reasoning in ADFs to QBFs, that can be used as the basis for novel systems for ADF reasoning.

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Section: Resultsmentioning

confidence: 99%

Reasoning in abstract dialectical frameworks using quantified Boolean formulas

Diller¹,

Wallner²,

Woltran³

2015

Argument & Computation

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“…One of these techniques is proposed in [70] and then followed by recent works on certificate generation for resolution-based QBF solvers (e.g. [8,9,48,57]) and preprocessors [32,36]. Thus, an interesting subject of future work is integration of a DPLL-based QBF solver into the QMSU1 algorithm and comparison of its performance (in terms of speed and a core size) with performance of the currently implemented CEGAR-based core-producing QBF oracle.…”

Section: Discussionmentioning

confidence: 98%

“…In the assumption method, we require a QBF solver to accept a set of literals that must be true (assumptions). Further, if the formula is false, it returns a subset of these assumptions that are responsible for the formula being false [48]. Then, every soft clause c is adorned with a fresh literal ¬s c ∨ c, and the solver is called with the assumptions {s c |c ∈ φ S }.…”

Section: Core Extraction For Dpll-based Qbf Solvers Extracting Cores mentioning

confidence: 99%

Quantified maximum satisfiability

2015

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In recent years, there have been significant improvements in algorithms both for Quantified Boolean Formulas (QBF) and for Maximum Satisfiability (MaxSAT). This paper studies an optimization extension of QBF and considers the problem in a quantified MaxSAT setting. More precisely, the general QMaxSAT problem is defined for QBFs with a set of soft clausal constraints and consists in finding the largest subset of the soft constraints such that the remaining QBF is true. Two approaches are investigated. One is based on relaxing the soft clauses and performing an iterative search on the cost function. The other approach, which is the main contribution of the paper, is inspired by recent work on MaxSAT, and exploits the iterative identification of unsatisfiable cores. The paper investigates the application of these approaches to the two concrete problems of computing smallest minimal unsatisfiable subformulas (SMUS) and smallest minimal equivalent subformulas (SMES), decision versions of which are well-known problems in the second level of the polynomial hierarchy. Experimental results, obtained on representative problem instances, indicate that the core-guided approach for the SMUS and SMES problems outperforms the use of iterative search over the values of the cost function. More significantly, Alexey Ignatiev Constraints the core-guided approach to SMUS also outperforms the state-of-the-art SMUS extractor Digger.

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“…A critical issue is on keeping safe learned clauses in successive iterations of a core-guided algorithm [41]. Quantified Boolean Formula (QBF) solving has successfully been made incremental [35] and further applied to verification [39].…”

Section: Related Workmentioning

confidence: 99%

Incremental Cardinality Constraints for MaxSAT

Martins

Joshi

Manquinho

et al. 2014

Lecture Notes in Computer Science

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Abstract. Maximum Satisfiability (MaxSAT) is an optimization variant of the Boolean Satisfiability (SAT) problem. In general, MaxSAT algorithms perform a succession of SAT solver calls to reach an optimum solution making extensive use of cardinality constraints. Many of these algorithms are non-incremental in nature, i.e. at each iteration the formula is rebuilt and no knowledge is reused from one iteration to another. In this paper, we exploit the knowledge acquired across iterations using novel schemes to use cardinality constraints in an incremental fashion. We integrate these schemes with several MaxSAT algorithms. Our experimental results show a significant performance boost for these algorithms as compared to their non-incremental counterparts. These results suggest that incremental cardinality constraints could be beneficial for other constraint solving domains.

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Incremental QBF Solving

Cited by 16 publications

References 35 publications

Reasoning in abstract dialectical frameworks using quantified Boolean formulas

Reasoning in abstract dialectical frameworks using quantified Boolean formulas

Quantified maximum satisfiability

Incremental Cardinality Constraints for MaxSAT

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