Variational satisfiability solving: efficiently solving lots of related SAT problems

Abstract

Incremental satisfiability (SAT) solving is an extension of classic SAT solving that enables solving a set of related SAT problems by identifying and exploiting shared terms. However, using incremental solvers effectively is hard since performance is sensitive to the input order of subterms and results must be tracked manually. For analyses that generate sets of related SAT problems, such as those in software product lines, incremental solvers are either not used or their use is not clearly described in the literature. This paper translates the ordering problem to an encoding problem and automates the use of incremental solving. We introduce variational SAT solving, which differs from incremental solving by accepting all related problems as a single variational input and returning all results as a single variational output. Variational solving syntactically encodes differences in related SAT problems as local points of variation. With this syntax, our approach automates the interaction with the incremental solver and enables a method to automatically optimize sharing in the input. To evaluate these ideas, we formalize a variational SAT algorithm, construct a prototype variational solver, and perform an empirical analysis on two real-world datasets that applied incremental solvers to software evolution scenarios. We show, assuming a variational input, that the prototype solver scales better for these problems than four off-the-shelf incremental solvers while also automatically tracking individual results.