Successful SAT Encoding Techniques

Abstract

This article identifies good practices for SAT encodings by analysing interviews with a number of well known SAT experts. The purpose is both to determine the confidence in different encoding strategies, by analysing whether there is consensus among the experts or not, as well as bringing out hidden knowledge to SAT users. There is consensus that encoding techniques usually have a dramatic impact on the efficiency of the SAT solver, that it often takes much work to find a good encoding, and that the size of an encoding is only very loosely related to the hardness of finding a solution. Topics where the interviewees disagree include the feasibility of including arithmetics in SAT problems and whether to formulate problems as clauses or circuits. The article describes a number of strategies that are good in different situations, such as different ways to represent numbers and how to use incrementality.