Amit Metodi

Compiling finite domain constraints to sat with bee

BEE is a compiler which facilitates solving finite domain constraints by encoding them to CNF and applying an underlying SAT solver. In BEE 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. We term this process equi-propagation. A key factor is that considering only a small fragment of a constraint model at one time enables to apply stronger, and even complete reasoning to detect equivalent literals in that fragment. Once detected, equivalences propagate to simplify the entire constraint model and facilitate further reasoning on other fragments. BEE is described in several recent papers. In this paper, after a quick review of BEE, we elaborate on two undocumented details of the implementation: the hybrid encoding of cardinality constraints and complete equi-propagation. We thendescribe on-going work aimed to extend BEE to consider binary representation of numbers.

Boolean equi-propagation for concise and efficient SAT encodings of combinatorial problems

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.

Boolean equi-propagation for optimized SAT encoding

We present an approach to propagation based SAT encoding, Boolean equi-propagation, where constraints are modelled as Boolean functions which propagate information about equalities between Boolean literals. This information is then applied as a form of partial evaluation to simplify constraints prior to their encoding as CNF formulae. We 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.

A novel SAT-based approach to model based diagnosis

This paper introduces a novel encoding of Model Based Diagnosis (MBD) to Boolean Satisfaction (SAT) focusing on minimal cardinality diagnosis. The encoding is based on a combination of sophisticated MBD preprocessing algorithms and the application of a SAT compiler which optimizes the encoding to provide more succinct CNF representations than obtained with previous works. Experimental evidence indicates that our approach is superior to all published algorithms for minimal cardinality MBD. In particular, we can determine, for the first time, minimal cardinality diagnoses for the entire standard ISCAS-85 and 74XXX benchmarks. Our results open the way to improve the state-of-the-art on a range of similar MBD problems.

Backbones for Equality

This paper generalizes the notion of the backbone of a CNF formula to capture also equations between literals. Each such equation applies to remove a variable from the original formula thus simplifying the formula without changing its satisfiability, or the number of its satisfying assignments. We prove that for a formula with n variables, the generalized backbone is computed with at most n + 1 satisfiable calls and exactly one unsatisfiable call to the SAT solver. We illustrate the integration of generalized backbone computation to facilitate the encoding of finite domain constraints to SAT. In this context generalized backbones are computed for small groups of constraints and then propagated to simplify the entire constraint model. A preliminary experimental evaluation is provided.