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, ≤) and as the vertex set of any graph G. Our algorithm, abbreviated All-Independent-Ideals (A-I-I), enumerates all G-independent ideals of (W, ≤). Since every satisfiable Boolean 2-Conjunctive Normal Form (CNF) can be Horn-renamed, A-I-I becomes the core of a polynomial total time algorithm that enumerates the modelset of any Boolean 2-CNF. As a perk, the modelset is delivered in a compressed format (that uses don't-care symbols)