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.

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.

This paper introduces an 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 SAT compilation techniques which together provide concise CNF formula. 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 benchmark. Our results open the way to improve the state-of-the-art on a range of similar MBD problems.

Abstract We presentBEE, a compiler which enables to encode finite domain constraint problems to CNF. UsingBEEboth eases the encoding process for the user and also performs transformations to simplify constraints and optimize their encoding to CNF. These optimizations are based primarily on equi-propagation and on partial evaluation, and also on the idea that a given constraint may have various possible CNF encodings. Often, the better encoding choice is made after constraint simplification.BEEis written in Prolog and integrates directly with a SAT solver through a suitable Prolog interface. We demonstrate that constraint simplification is often highly beneficial when solving hard finite domain constraint problems. ABEEimplementation is available with this paper.