Efficiently grounding FOL using bit vectors

Abstract

Several paradigms for declarative problem solving start from a specification in a high-level language, which is then transformed to a low-level language, such as SAT or SMT. Often, this transformation includes a "grounding" step to remove first-order quantification. To reduce the time and size of the grounding, it can be useful to simplify formulas along the way, e.g., by already taking into account the interpretation of symbols that are already known. In this paper, we investigate the use of bit vectors to efficiently simplify formulas, thereby taking advantage of the fact that, on modern hardware, logical operations on bit vectors can be executed extremely fast. We conduct an experimental analysis, which shows that bit vectors are indeed fast for certain problems, but also have limitations.