Inst-Gen – A Modular Approach to Instantiation-Based Automated Reasoning

Korovin, Konstantin

doi:10.1007/978-3-642-37651-1_10

Cited by 52 publications

(51 citation statements)

References 43 publications

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“…This is the case if and only if no pair of oppositely signed, selected (satisfying) literals corresponds to the same existential variable in overlapping contexts. For EPR, this is exactly what happens in the Inst-Gen calculus when there is a check on whether the corresponding literals can be unified [22,23,24]. In the case that a satisfying assignment is valid for the current set of clause instances, we know that the original DQBF is satisfiable.…”

Section: Idq Architecturementioning

confidence: 93%

“…In the following, we sometimes use the shorter notation φ u and φ u instead of φ u=1 and φ u=0 , respectively. We also extend this notation to clauses in the same way as we introduced it for formulas and refer to this as a clause instance, in the sense the Inst-Gen calculus [23,24] uses instantiation, applied to the natural encoding of (D)QBF into first-order logic [35]. Furthermore, for a given clause instance C l1,...,l k , we define ctx(C l1,...,l k ) := {l i | i = 1, .…”

Section: Preliminariesmentioning

confidence: 99%

“…Figure 1: Pseudo-code of a CEGAR loop as used in the Inst-Gen procedure [22,23,24]. calls depending on the order of the quantifier prefix, an extension to DQBF does not seem to be straightforward.…”

Section: Preliminariesmentioning

confidence: 99%

“…It is based on the more general Inst-Gen calculus [23,24] for EPR as used in iProver [22], but reduced to the more specific case of DQBF. Instead of dealing with predicates, we use the notion of clause instances as introduced in Sect.…”

Section: Idq Architecturementioning

confidence: 99%

“…Our approach is closely related to the so-called Inst-Gen calculus [23,24], which can be considered as the state-of-the-art decision procedure for EPR [22]. While DQBF can be translated to EPR, we focus on applying the decision procedure directly on the given input logic.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

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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Section: Idq Architecturementioning

confidence: 93%

Section: Preliminariesmentioning

confidence: 99%

Section: Preliminariesmentioning

confidence: 99%

Section: Idq Architecturementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

iDQ: Instantiation-Based DQBF Solving

Fröhlich¹,

Kovásznai²,

Biere³

et al.

EPiC Series in Computing

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On the Expressivity and Applicability of Model Representation Formalisms

Teucke

Voigt

Weidenbach

2019

Frontiers of Combining Systems

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A number of first-order calculi employ an explicit model representation formalism for automated reasoning and for detecting satisfiability. Many of these formalisms can represent infinite Herbrand models. The first-order fragment of monadic, shallow, linear, Horn (MSLH) clauses, is such a formalism used in the approximation refinement calculus. Our first result is a finite model property for MSLH clause sets. Therefore, MSLH clause sets cannot represent models of clause sets with inherently infinite models. Through a translation to tree automata, we further show that this limitation also applies to the linear fragments of implicit generalizations, which is the formalism used in the model-evolution calculus, to atoms with disequality constraints, the formalisms used in the non-redundant clause learning calculus (NRCL), and to atoms with membership constraints, a formalism used for example in decision procedures for algebraic data types. Although these formalisms cannot represent models of clause sets with inherently infinite models, through an additional approximation step they can. This is our second main result. For clause sets including the definition of an equivalence relation with the help of an additional, novel approximation, called reflexive relation splitting, the approximation refinement calculus can automatically show satisfiability through the MSLH clause set formalism.

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SCL Clause Learning from Simple Models

Fiori

Weidenbach

2019

Lecture Notes in Computer Science

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Several decision procedures for the Bernays-Schoenfinkel (BS) fragment of first-order logic rely on explicit model assumptions. In particular, the procedures differ in their respective model representation formalisms. We introduce a new decision procedure SCL deciding the BS fragment. SCL stands for clause learning from simple models. Simple models are solely built on ground literals. Nevertheless, we show that SCL can learn exactly the clauses other procedures learn with respect to more complex model representation formalisms. Therefore, the overhead of complex model representation formalisms is not always needed. SCL is sound and complete for full first-order logic without equality. This paper was published at CADE-27 [7].

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Inst-Gen – A Modular Approach to Instantiation-Based Automated Reasoning

Cited by 52 publications

References 43 publications

iDQ: Instantiation-Based DQBF Solving

iDQ: Instantiation-Based DQBF Solving

On the Expressivity and Applicability of Model Representation Formalisms

SCL Clause Learning from Simple Models

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