Generating Difficult SAT Instances by Preventing Triangles

Abstract: When creating benchmarks for SAT solvers, we need SAT instances that are easy to build but hard to solve. A recent development in the search for such methods has led to the Balanced SAT algorithm, which can create k-SAT instances with m clauses of high difficulty, for arbitrary k and m. In this paper we introduce the No-Triangle SAT algorithm, a SAT instance generator based on the cluster coefficient graph statistic. We empirically compare the two algorithms by fixing the arity and the number of variables, but varying the number of clauses. The hardest instances that we find are produced by No-Triangle SAT. Furthermore, difficult instances from No-Triangle SAT have a different number of clauses than difficult instances from Balanced SAT, potentially allowing a combination of the two methods to find hard SAT instances for a larger array of parameters.