P.: Optimal base encodings for pseudoBoolean constraints

Abstract. This paper formalizes the optimal base problem, presents an algorithm to solve it, and describes its application to the encod-ing of Pseudo-Boolean constraints to SAT. We demonstrate the im-pact of integrating our algorithm within the Pseudo-Boolean constraint solver MiniSat+. Experimentation indicates that our algorithm scales to bases involving numbers up to 1,000,000, improving on the restriction in MiniSat+ to prime numbers up to 17. We show that, while for many examples primes up to 17 do suffice, encoding with respect to optimal bases reduces the CNF sizes and improves the subsequent SAT solving time for many examples.