Efficient CNF Simplification Based on Binary Implication Graphs

Abstract

Abstract. This paper develops techniques for efficiently detecting redundancies in CNF formulas. We introduce the concept of hidden literals, resulting in the novel technique of hidden literal elimination. We develop a practical simplification algorithm that enables "Unhiding" various redundancies in a unified framework. Based on time stamping literals in the binary implication graph, the algorithm applies various binary clause based simplifications, including techniques that, when run repeatedly until fixpoint, can be too costly. Unhiding can also be applied during search, taking learnt clauses into account. We show that Unhiding gives performance improvements on real-world SAT competition benchmarks.

Learning from conflicts in propositional satisfiability

“…At each conflict, it exploits clause learning to subsume clauses of the original formula and of the learnt clauses database. Designing strong preprocessing techniques able to greatly reduce the size of the formula remains an important research issue (see for example recent works by Heule et al 2010Heule et al , 2011Piette et al 2008). …”

Conditional Lower Bounds for Failed Literals and Related Techniques

“…If is an asymmetric tautology in C, then F can be simplified by letting F := (F \ C) ∧ (C \ l). The notion of asymmetric literals is a generalization of hidden literals [20]. Both asymmetric tautologies and asymmetric literals are detected e.g.…”

“…Unit propagation is a common basis for many different simplification techniques [3,12,13,17,18,20,21,31,32,35,38]. A key example is failed literal elimination [13,31,34], which aims at deducing unit clauses via checking whether assuming a truth value for a single variable results in a conflict by unit propagation.…”

On Preprocessing Techniques and Their Impact on Propositional Model Counting

“…It proves useful when the problem under consideration (e.g., the satisfiability issue) can be solved more efficiently when the input formula has been first preprocessed (while taking account for the preprocessing time in the global solving time). Some preprocessing techniques are nowadays acknowledged as valuable for sat solving and qbf solving (see e.g., [5,22,26,27,29,32,37,46,53]), leading to computational improvements. Let us mention among others the following techniques:…”