Efficiently solving quantified bit-vector formulas

Wintersteiger, Christoph M.; Hamadi, Youssef; Moura, Leonardo de

doi:10.1007/s10703-012-0156-2

Cited by 69 publications

(62 citation statements)

References 4 publications

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“…In [12,13], the quantified case is addressed, and the satisfiability problem of this logic with uninterpreted functions (UFBV) is proved to be NExpTime-complete. Again, the proof only holds if we assume unary encoded bit-widths.…”

Section: Introductionmentioning

confidence: 99%

More on the Complexity of Quantifier-Free Fixed-Size Bit-Vector Logics with Binary Encoding

Fröhlich

Kovásznai

Biere

2013

Computer Science – Theory and Applications

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Abstract. Bit-precise reasoning is important for many practical applications of Satisfiability Modulo Theories (SMT). In recent years, efficient approaches for solving fixed-size bit-vector formulas have been developed. From the theoretical point of view, only few results on the complexity of fixed-size bit-vector logics have been published. Most of these results only hold if unary encoding on the bit-width of bit-vectors is used. In previous work [1], we showed that binary encoding adds more expressiveness to bit-vector logics, e.g. it makes fixed-size bit-vector logic without uninterpreted functions nor quantification NExpTime-complete. In this paper, we look at the quantifier-free case again and propose two new results. While it is enough to consider logics with bitwise operations, equality, and shift by constant to derive NExpTime-completeness, we show that the logic becomes PSpace-complete if, instead of shift by constant, only shift by 1 is permitted, and even NP-complete if no shifts are allowed at all.

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Section: Introductionmentioning

confidence: 99%

More on the Complexity of Quantifier-Free Fixed-Size Bit-Vector Logics with Binary Encoding

Fröhlich

Kovásznai

Biere

2013

Computer Science – Theory and Applications

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“…Decision procedures for quantified propositional formulas on bit as well as word level [24,34] rely on iteration and refinement for the discovery of witnesses. The possibility of integration of QBF solvers as an implementation of EncodeValidity is an interesting avenue for future research.…”

Section: Related Workmentioning

confidence: 99%

Solving Existentially Quantified Horn Clauses

Beyene

Popeea

Rybalchenko

2013

Computer Aided Verification

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Abstract. Temporal verification of universal (i.e., valid for all computation paths) properties of various kinds of programs, e.g., procedural, multi-threaded, or functional, can be reduced to finding solutions for equations in form of universally quantified Horn clauses extended with well-foundedness conditions. Dealing with existential properties (e.g., whether there exists a particular computation path), however, requires solving forall-exists quantified Horn clauses, where the conclusion part of some clauses contains existentially quantified variables. For example, a deductive approach to CTL verification reduces to solving such clauses. In this paper we present a method for solving forall-exists quantified Horn clauses extended with well-foundedness conditions. Our method is based on a counterexample-guided abstraction refinement scheme to discover witnesses for existentially quantified variables. We also present an application of our solving method to automation of CTL verification of software, as well as its experimental evaluation.

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“…The idea of instantiating (multiple) instances of Boolean formulae with models can be seen as a form of circuit co-factoring as described by Ganai et al [15]. A recent contribution to reasoning about quantified bit-vector formulae was made by Wintersteiger et al [36], who most notably used word-level simplifications and template instantiations.…”

Section: Related Workmentioning

confidence: 99%

Approximate Quantifier Elimination for Propositional Boolean Formulae

Brauer

King²

2011

Lecture Notes in Computer Science

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Abstract. This paper describes an approximate quantifier elimination procedure for propositional Boolean formulae. The method is based on computing prime implicants using SAT and successively refining overapproximations of a given formula. This construction naturally leads to an anytime algorithm, that is, it can be interrupted at anytime without compromising soundness. This contrasts with classical monolithic (all or nothing) approaches based on resolution or model enumeration.

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Efficiently solving quantified bit-vector formulas

Cited by 69 publications

References 4 publications

More on the Complexity of Quantifier-Free Fixed-Size Bit-Vector Logics with Binary Encoding

More on the Complexity of Quantifier-Free Fixed-Size Bit-Vector Logics with Binary Encoding

Solving Existentially Quantified Horn Clauses

Approximate Quantifier Elimination for Propositional Boolean Formulae

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