Variable and Term Removal From Boolean Formulae

Boolean-valued Term Models

We construct Boolean-valued term models and describe their universal properties. The underlying set of these models consists of the terms of the underlying language, while formulae are interpreted in the Lindenbaum-Tarski algebra of open formulae. Subspaces of the Stone space of the Lindenbaum-Tarski algebra of open formulae are shown to be homeomorphic to spaces of enumerated models models equ...

Discovering the Impact of Group Structure on 3-SAT

Boolean SAT problems are widespread in current demanding applications, most notably model checking for both hardware and software. It has long been known that the clause-to-variable ratio describes the likely behavior of randomly generated boolean formulae. This paper empirically investigates how the grouping of variables in these formulae further affects their satisfiability. keywords: normali...

Solving 2-CNF Quantified Boolean Formulae Using Variable Assignment and Propagation

Variable Compression in ProbLog

The paper identifies patterns of Boolean variables that occur in Boolean formulae, namely AND-clusters and OR-clusters. We give a polynomial algorithm that detects AND-clusters in disjunctive normal form (DNF) Boolean formulae, or OR-clusters in conjunctive normal form (CNF) Boolean formulae. Furthermore, we explain how to exploit the clusters in the context of ProbLog. In ProbLog, Boolean form...

#2,2-sat Is Solvable in Linear-time

A linear-time algorithm, with respect to the size of the instance Boolean formula, is presented for the #SAT problem restricted to formulae of the form #2; 2-CF, i.e. formulae whose clauses have just two literals and in which each variable appears at most twice.