Nested Boolean Functions as Models for Quantified Boolean Formulas

Bubeck, Uwe; Büning, Hans Kleine

doi:10.1007/978-3-642-39071-5_20

Cited by 5 publications

(4 citation statements)

References 7 publications

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“…Both definitions are ultimately equivalent in the sense that a winning strategy according to one definition can be transformed into a winning strategy according to the other definition without changing its responses (cf. the work on quantifier elimination by functional composition and selfsubstitution [8,14,28,29]). One can prove an analogue of Proposition 1 stating that the strategy function-according to the alternative definition-of a variable x is unique whenever x is defined in terms of the variables preceding x in the quantifier prefix.…”

Section: Improvements and Generalization To Dependency Qbfmentioning

confidence: 99%

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Interpolation-Based Semantic Gate Extraction and Its Applications to QBF Preprocessing

Slivovsky

2020

Computer Aided Verification

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We present a new semantic gate extraction technique for propositional formulas based on interpolation. While known gate detection methods are incomplete and rely on pattern matching or simple semantic conditions, this approach can detect any definition entailed by an input formula. As an application, we consider the problem of computing unique strategy functions from Quantified Boolean Formulas (QBFs) and Dependency Quantified Boolean Formulas (DQBFs). Experiments with a prototype implementation demonstrate that functions can be efficiently extracted from formulas in standard benchmark sets, and that many of these definitions remain undetected by syntactic gate detection. We turn this into a preprocessing technique by substituting unique strategy functions for input variables and test solver performance on the resulting instances. Compared to syntactic gate detection, we see a significant increase in the number of solved QBF instances, as well as a modest increase for DQBF instances.

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Section: Improvements and Generalization To Dependency Qbfmentioning

confidence: 99%

“…Table 1 (left) shows quartiles for the distributions of unique existential strategy functions detected by Unique in each benchmark set. 8 We only show the distribution for existential variables in Table 1 and Fig. 2 since very few universal variables were found to have unique strategy functions.…”

Section: Gate Extractionmentioning

confidence: 99%

Interpolation-Based Semantic Gate Extraction and Its Applications to QBF Preprocessing

Slivovsky

2020

Computer Aided Verification

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“…Developing methods for NC reasoning is an actual concern in the principlal fields of classical logic, namely satisfiability solving [54,43], logic programming [17,14], theorem proving [31,53] and quantified boolean formulas [30,13], and in many other fields (see [40] and the references thereof). And within non-classical logics, NC formulas with different functionalities have been studied in a profusion of languages: signed many-valued logic [47,8,58], Lukasiewicz logic [42], Levesque's three-valued logic [15], Belnap's four-valued logic [15], M3 logic [1], fuzzy logic [35], fuzzy description logic [34], intuitionistic logic [55], modal logic [55], lattice-valued logic [60] and regular many-valued logic [39].…”

Section: Introductionmentioning

confidence: 99%

The Possibilistic Horn Non-Clausal Knowledge Bases

Imaz¹

2021

Preprint

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Posibilistic logic is the most extended approach to handle uncertain and partially inconsistent information. Regarding normal forms, advances in possibilistic reasoning are mostly focused on clausal form. Yet, the encoding of real-world problems usually results in a non-clausal (NC) formula and NC-to-clausal translators produce severe drawbacks that heavily limit the practical performance of clausal reasoning. Thus, by computing formulas in its original NC form, we propose several contributions showing that notable advances are also possible in possibilistic non-clausal reasoning.Firstly, we define the class of Possibilistic Horn Non-Clausal Knowledge Bases, or H Σ , which subsumes the classes: possibilistic Horn and propositional Horn-NC. H Σ is shown to be a kind of NC analogous of the standard Horn class.Secondly, we define Possibilistic Non-Clausal Unit-Resolution, or UR Σ , and prove that UR Σ correctly computes the inconsistency degree of H Σ members. UR Σ had not been proposed before and is formulated in a clausal-like manner, which eases its understanding, formal proofs and future extension towards non-clausal resolution.Thirdly, we prove that computing the inconsistency degree of H Σ members takes polynomial time. Although there already exist tractable classes in possibilistic logic, all of them are clausal, and thus, H Σ turns out to be the first characterized polynomial non-clausal class within possibilistic reasoning.We discuss that our approach serves as a starting point to developing uncertain non-clausal reasoning on the basis of both methodologies: DPLL and resolution.

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“…Certificate construction in QBF has seen increasing interest in recent research [8,12,18,19,21,30,36,37]. While providing certificates is not implemented in our prototype yet, our architecture can easily be extended by this feature.…”

Section: Resultsmentioning

confidence: 99%

iDQ: Instantiation-Based DQBF Solving

Fröhlich¹,

Kovásznai²,

Biere³

et al.

EPiC Series in Computing

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Dependency Quantified Boolean Formulas (DQBF) are obtained by adding Henkin quantifiers to Boolean formulas and have seen growing interest in the last years. Since deciding DQBF is NExpTime-complete, efficient ways of solving it would have many practical applications. Still, there is only few work on solving this kind of formulas in practice. In this paper, we present an instantiation-based technique to solve DQBF efficiently. Apart from providing a theoretical foundation, we also propose a concrete implementation of our algorithm. Finally, we give a detailed experimental analysis evaluating our prototype iDQ on several DQBF as well as QBF benchmarks.

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Nested Boolean Functions as Models for Quantified Boolean Formulas

Cited by 5 publications

References 7 publications

Interpolation-Based Semantic Gate Extraction and Its Applications to QBF Preprocessing

Interpolation-Based Semantic Gate Extraction and Its Applications to QBF Preprocessing

The Possibilistic Horn Non-Clausal Knowledge Bases

iDQ: Instantiation-Based DQBF Solving

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