Blocked Clause Decomposition

Abstract

Abstract. We demonstrate that it is fairly easy to decompose any propositional formula into two subsets such that both can be solved by blocked clause elimination. Such a blocked clause decomposition is useful to cheaply detect backbone variables and equivalent literals. Blocked clause decompositions are especially useful when they are unbalanced, i.e., one subset is much larger in size than the other one. We present algorithms and heuristics to obtain unbalanced decompositions efficiently. Our techniques have been implemented in the state-of-the-art solver Lingeling. Experiments show that the performance of Lingeling is clearly improved due to these techniques on application benchmarks of the SAT Competition 2013.

Everything You Always Wanted to Know about Blocked Sets (But Were Afraid to Ask)

“…In this paper, we revisit topics from previous work [5] and present several new results. The paper is structured as follows.…”

“…In this section, we revisit two monotonicity properties of blocked sets from previous work [5,4] and then prove several new properties. One basic property of blocked sets is the following monotonicity property: If G ⊂ F and C is blocked w.r.t.…”

“…F , then C is blocked w.r.t. G [5,4]. A direct implication is given by the following second version: If F ∈ BS and G ⊆ F then G ∈ BS.…”

“…Conjunctive normal form (CNF) level simplification techniques, such as blocked clause elimination (BCE) [2,3,4], play an important role in the solving process. A novel use of blocked clauses was proposed in [5], which showed, that it is possible to decompose any propositional formula into two so called blocked sets, both of which can be solved solely by blocked clause elimination. This blocked clause decomposition was then used to efficiently find backbone variables [6] and implied binary equivalences through SAT sweeping.…”

“…In Sect. 5, we revisit blocked clause decomposition (BCD), as earlier proposed in [5], and suggest extensions to increase performance of decomposition algorithms and to generate blocked sets with certain useful attributes. We apply these techniques in Sect.…”