Interpolant based Decision Procedure for Quantifier-Free Presburger Arithmetic

Lahiri, Shuvendu K.; Mehra, Krishna Kumar

doi:10.3233/sat190011

Cited by 3 publications

(4 citation statements)

References 35 publications

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“…A technique that is frequently employed to speed up the solving process for hard instances is abstraction [5,6,20,7,8,3,25]. Instead of the original problem, a related problem is analyzed that is supposed to be easier to solve.…”

Section: Introductionmentioning

confidence: 99%

“…Brummayer and Biere [5,6] applied this technique to the theory of bit-vectors and arrays, and combined it with under-approximations via bitwidthreduction. Lahiri and Mehra [20] developed an algorithm combining underand over-approximations for the theory of quantifier-free Presburger arithmetic (QFP) based on interpolation. Bryant et al [7] present an approach where formulae in bit-vector logic are encoded with fewer Boolean variables than their width, resulting in an under-approximation.…”

Section: Introductionmentioning

confidence: 99%

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An Incremental Abstraction Scheme for Solving Hard SMT-Instances over Bit-Vectors

Teuber¹,

Büning²,

Sinz³

2020

Preprint

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Decision procedures for SMT problems based on the theory of bit-vectors are a fundamental component in state-of-the-art software and hardware verifiers. While very efficient in general, certain SMT instances are still challenging for state-of-the-art solvers (especially when such instances include computationally costly functions). In this work, we present an approach for the quantifier-free bit-vector theory (QF_BV in SMT-LIB) based on incremental SMT solving and abstraction refinement. We define four concrete approximation steps for the multiplication, division and remainder operators and combine them into an incremental abstraction scheme. We implement this scheme in a prototype extending the SMT solver Boolector and measure both the overall performance and the performance of the single approximation steps. The evaluation shows that our abstraction scheme contributes to solving more unsatisfiable benchmark instances, including seven instances with unknown status in SMT-LIB.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

An Incremental Abstraction Scheme for Solving Hard SMT-Instances over Bit-Vectors

Teuber¹,

Büning²,

Sinz³

2020

Preprint

View full text Add to dashboard Cite

show abstract

“…To prove program properties over a combination of data structures, such as integers, arrays and pointers, several approaches based on theory-specific reasoning have been proposed, see e.g. [14,5,4]. While powerful, these techniques are limited to quantifier-free fragments of first-order logic.…”

Section: Introductionmentioning

confidence: 99%

Splitting Proofs for Interpolation

Gleiss

Kovács

Suda

2017

Automated Deduction – CADE 26

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We study interpolant extraction from local first-order refutations. We present a new theoretical perspective on interpolation based on clearly separating the condition on logical strength of the formula from the requirement on the common signature. This allows us to highlight the space of all interpolants that can be extracted from a refutation as a space of simple choices on how to split the refutation into two parts. We use this new insight to develop an algorithm for extracting interpolants which are linear in the size of the input refutation and can be further optimized using metrics such as number of non-logical symbols or quantifiers. We implemented the new algorithm in first-order theorem prover VAMPIRE and evaluated it on a large number of examples coming from the first-order proving community. Our experiments give practical evidence that our work improves the state-of-the-art in first-order interpolation.

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“…In an effort to combine eager and lazy methods such as ASAP [7], ranges are underestimated and iteratively increased until a solution is found or the formula is proved unsatisfiable. A related approach is followed in [28]. The problem encoded after range refinement can be quite different structurally from that before the refinement.…”

Section: Introductionmentioning

confidence: 99%

SDSAT: Tight Integration of Small Domain Encoding and Lazy Approaches in Solving Difference Logic

Ganai

Talupur

Gupta

2007

SAT

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Existing difference logic (DL) solvers can be broadly classified as eager or lazy, each with its own merits and de-merits. We propose a novel difference logic solver SDSAT that combines the strengths of both these approaches and provides a robust performance over a wide set of benchmarks. The solver SDSAT works in two phases: allocation and solve. In the allocation phase, it allocates non-uniform adequate ranges for variables appearing in difference predicates. This phase is similar to previous small domain encoding approaches, but uses a novel algorithm Nu-SMOD with 1-2 orders of magnitude improvement in performance and smaller ranges for variables. Furthermore, the difference logic formula is not transformed into an equi-satisfiable Boolean formula in a single step, but rather done lazily in the following phase. In the solve phase, SDSAT uses a lazy refinement approach to search for a satisfying model within the allocated ranges. Thus, any partially DL-theory consistent model can be discarded if it cannot be satisfied within the allocated ranges. Note the crucial difference: in eager approaches, such a partially consistent model is not allowed in the first place, while in lazy approaches such a model is never discarded. Moreover, we dynamically refine the allocated ranges and search for a feasible solution within the updated ranges. This combined approach benefits from both the smaller search space (as in eager approaches) and also from the theory-specific graph-based algorithms (characteristic of lazy approaches). Experimental results show that our method is robust and always better than or comparable to state-of-the art solvers using similar eager or lazy techniques.

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Interpolant based Decision Procedure for Quantifier-Free Presburger Arithmetic

Cited by 3 publications

References 35 publications

An Incremental Abstraction Scheme for Solving Hard SMT-Instances over Bit-Vectors

An Incremental Abstraction Scheme for Solving Hard SMT-Instances over Bit-Vectors

Splitting Proofs for Interpolation

SDSAT: Tight Integration of Small Domain Encoding and Lazy Approaches in Solving Difference Logic

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