Towards a Compact and Efficient SAT-Encoding of Finite Linear CSP

This paper describes a new SAT encoding method applicable to finite linear CSP, named compact order encoding, which is designed to generate compact (small sized) and also efficient SAT instances. The basic idea of the compact order encoding is the use of a numeric system of base B ≥ 2. Each integer variable is divided into m digits and each digit is encoded by using the order encoding. Therefore, it is a generalization of the order encoding (when m = 1), and the log encoding (when B = 2). In the compact order encoding, each binary constraint can be encoded into O(B logB d) SAT clauses which is much less than O(d) clauses of the order encoding where d is the maximum domain size. Therefore it enables to solve large problems that can not be solved by the order encoding. The compact order encoding can generate much efficient SAT instance than the log encoding in general because it uses fewer digits and enables faster propagations. We also confirmed these observations through some experimental results.