Optimizing SAT Encodings for Arithmetic Constraints

The log encoding has been perceived to be unsuited to arithmetic constraints due to its hindrance to propagation. The surprising performance of PicatSAT, which is a pure eager SAT compiler based on the log encoding, in the MiniZinc Challenge 2016 has revived interest in the log encoding. This paper details the optimizations used in PicatSAT for encoding arithmetic constraints. PicatSAT adopts some well-known optimizations from CP systems, language compilers, and hardware design systems for encoding constraints into compact and efficient SAT code. PicatSAT is also empowered by a novel optimization, called equivalence reasoning, for arithmetic constraints, which leads to reduction of code size and execution time. In a nutshell, this paper demonstrates that the optimized log encoding is competitive for encoding arithmetic constraints.