Blocked Clause Elimination

Abstract

Abstract. Boolean satisfiability (SAT) and its extensions are becoming a core technology for the analysis of systems. The SAT-based approach divides into three steps: encoding, preprocessing, and search. It is often argued that by encoding arbitrary Boolean formulas in conjunctive normal form (CNF), structural properties of the original problem are not reflected in the CNF. This should result in the fact that CNF-level preprocessing and SAT solver techniques have an inherent disadvantagecompared to related techniques applicable on the level of more structural SAT instance representations such as Boolean circuits. In this work we study the effect of a CNF-level simplification technique called blocked clause elimination (BCE). We show that BCE is surprisingly effective both in theory and in practice on CNFs resulting from a standard CNF encoding for circuits: without explicit knowledge of the underlying circuit structure, it achieves the same level of simplification as a combination of circuit-level simplifications and previously suggested polarity-based CNF encodings. Experimentally, we show that by applying BCE in preprocessing, further formula reduction and faster solving can be achieved, giving promise for applying BCE to speed up solvers.

Efficient CNF Simplification Based on Binary Implication Graphs

“…In other words, UHLE could in some cases disrupt UHTE. For instance, consider the clause (a ∨ b ∨ c) and the following time stamps: a : [2,3],ā : [9,10], b : [1,4],b : [5,8], c : [6,7],c : [11,12]. Now UHLE removes literal b which is required for UHTE to return true.…”

“…Due to symmetry, there is only one possible DFS traversal order, and it produces the time stamps a : [1,8],b : [2,3],c : [4,5],d : [6,7], b : [9,12],ā : [10,11], c : [13,14], d : [15,16]. Only three of the six binary clauses are represented by the time stamps.…”

“…[1,2,3,4,5,6,7]) to simplify Boolean satisfiability (SAT) instances both before and during search is important for improving stateof-the-art SAT solvers. This paper develops techniques for efficiently detecting and removing redundancies from CNF (conjunctive normal form) formulas based on the underlying binary clause structure (i.e., the binary implication graph) of the formulas.…”

Exact DFA Identification Using SAT Solvers

“…We will show that these blocked clauses improve the performance of DFA identification. However, for other problems, removal of blocked clauses results in a speed-up [18].…”

Unsatisfiability Proofs for Parallel SAT Solver Portfolios with Clause Sharing and Inprocessing

“…Several formula simplification techniques were proposed, including the following ones, that can be characterized in terms of RAT: bounded variable elimination and addition [11,32,41,45], blocked clause elimination [25], blocked clause addition [26,28], equivalent literal elimination [13], probing [31], extended resolution and reencoding [32,46], symmetry breaking [10,17], and BDDbased reasoning [44].…”