Boolean Equi-propagation for Optimized SAT Encoding

Metodi, Amit; Codish, Michael; Lagoon, Vitaly; Stuckey, Peter J.

doi:10.1007/978-3-642-23786-7_47

Cited by 13 publications

(13 citation statements)

References 16 publications

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“…This paper extends earlier work presented by Metodi, Codish, Lagoon, and Stuckey (2011), which first introduced equi-propagation, and also the BEE tool paper (Metodi & Codish, 2012). The BEE tool is available for download (Metodi, 2012).…”

Section: Introductionsupporting

confidence: 58%

Boolean Equi-propagation for Concise and Efficient SAT Encodings of Combinatorial Problems

Metodi¹,

Codish²,

Stuckey³

2013

jair

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We present an approach to propagation-based SAT encoding of combinatorial problems, Boolean equi-propagation, where constraints are modeled as Boolean functions which propagate information about equalities between Boolean literals. This information is then applied to simplify the CNF encoding of the constraints. A key factor is that considering only a small fragment of a constraint model at one time enables us to apply stronger, and even complete, reasoning to detect equivalent literals in that fragment. Once detected, equivalences apply to simplify the entire constraint model and facilitate further reasoning on other fragments. Equi-propagation in combination with partial evaluation and constraint simplification provide the foundation for a powerful approach to SAT-based finite domain constraint solving. We introduce a tool called BEE (Ben-Gurion Equi-propagation Encoder) based on these ideas and demonstrate for a variety of benchmarks that our approach leads to a considerable reduction in the size of CNF encodings and subsequent speed-ups in SAT solving times.

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Section: Introductionsupporting

confidence: 58%

Boolean Equi-propagation for Concise and Efficient SAT Encodings of Combinatorial Problems

Metodi¹,

Codish²,

Stuckey³

2013

jair

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“…In [MCLS11], the authors observe an additional property of the order encoding: its ability to specify that a variable cannot take a specific value 1 ≤ v ≤ k in its domain by equating two variables: x v = x v+1 . This indicates that the order encoding is well-suited not only to propagate lower and upper bounds, but also to represent integer variables with an arbitrary finite domain.…”

Section: Exotic Order Encodingmentioning

confidence: 99%

“…It combines constraint and CNF simplification techniques to provide a concise CNF representation [MCLS11]. BEE uses the SAT solver Our experimentation initiates a comparison of these tools when solving exotic semiring constraints.…”

Section: Tools and Experimentsmentioning

confidence: 99%

“…4 using BEE [MCLS11] with SMT solving using Z3. SMT solvers with a dedicated theory solver like Z3 natively support all natural numbers as search space for the input constraint.…”

Section: Tools and Experimentsmentioning

confidence: 99%

“…However, size is not the only metric to regard for SAT encodings. Instead, in other applications [TTKB09,MCLS11] unary bitblasting has been shown to result in encodings which often lead to smaller runtimes of the SAT solver. In this paper, we propose a unary encoding based on the, so-called, order encoding (see e.g.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Exotic Semi-Ring Constraints

Codish

Fekete

Fuhs

et al.

EPiC Series in Computing

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Exotic semiring constraints arise in a variety of applications and in particular in the context of automated termination analysis. We propose two techniques to solve such constraints: (a) to model them using Boolean functions and integer linear arithmetic and solve them using an SMT solver (QF LIA, in certain cases also QF IDL); and (b) to seek finite domain solutions by applying unary bit-blasting and solve them using a SAT solver. In this note, we show the structure of such systems of constraints, and report on the performance of SMT solvers and SAT encodings when solving them. In particular, we observe that good results are obtained by unary bit-blasting, improving on previous proposals to apply binary bit-blasting. Moreover, our results indicate that, for our benchmarks, unary bit-blasting leads to better results than the ones directly obtained by an SMT solver.

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