Compression with wildcards: All models of a Boolean 2-CNF

Abstract

Let $W$ be a finite set which simultaneously serves as the universe of any poset $(W,\preceq)$ and as the vertex set of any graph $G$. Our algorithm, abbreviated A-I-I, enumerates (in a compressed format using don't-care symbols) all $G$-independent order ideals of $(W,\preceq)$. For many instances the high-end Mathematica implementation of A-I-I compares favorably to the hardwired Mathematica commands {\tt BooleanConvert} and {\tt SatisfiabilityCount}. The A-I-I can be parallelized and adapts to a polynomial total time algorithm that enumerates the modelset of any Boolean 2-CNF.