A new SAT Encoding Scheme for Exactly-one Constraints

Abstract

Exactly-one constraints have comprehensive applications for the fields of artificial intelligence and operations research. For many encoded SAT problems generated by the existing encoding schemes of exactly-one constraints, the state-of-the-art knowledge compilers cannot complete compilation. In this paper, we propose a new encoding scheme of exactly-one constraints. We introduce two-dimensional auxiliary variables (represented as a matrix) to denote the constraint that exactly one of some variables can be assigned as true. The clauses generated by our scheme is significantly less than those generated by three other existing encoding schemes. The experimental results on the exact cover problems show that the encoded CNF formulas generated by our scheme requires less compilation time, compared with the other three coding schemes.