On solving stack-based incremental satisfiability problems

Abstract

Boolean satisfiability (SAT) and its application to a number of electronic design automation (EDA) problems have been the topic of extensive study over the lost couple of decades. In many cases, a set of related SAT problems need to be solved in order to obtain an answer to a given application-specific problem. Incremental satisfiability (ISAT) refers to solving a set of related SAT problems by augmenting a previously solved problem with additional constraints, thereby reusing previous decision sequences. In this paper, we present a new ISAT engine that supports both the addition and removal of constraints. This can be achieved by keeping track of the relationships between constraints. We identify and define a special type of ISAT that occurs frequently in the context of path sensitization called stack-based ISAT and define the structure of this as a problem tree. In this type of ISAT constraints are allowed to be added and removed only in last-in first-out (LIFO) order. We also introduce a solution caching mechanism to expedite the search by recording and retrieving solutions to intermediate nodes in a problem tree.