The Community Structure of SAT Formulas

Abstract

Abstract. The research community on complex networks has developed techniques of analysis and algorithms that can be used by the SAT community to improve our knowledge about the structure of industrial SAT instances. It is often argued that modern SAT solvers are able to exploit this hidden structure, without a precise definition of this notion. In this paper, we show that most industrial SAT instances have a high modularity that is not present in random instances. We also show that successful techniques, like learning, (indirectly) take into account this community structure. Our experimental study reveal that most learnt clauses are local on one of those modules or communities.

Eigenvector Centrality in Industrial SAT Instances

“…But what exactly is this particular structure? It is understood that real world instances are different from uniform random instances, but only recently has some progress been made toward characterizing this structure by finding that these instances exhibit modularity [1,2]. It is also known [8] that many real-world instances share the small-world property of graphs.…”

A scalable community detection algorithm for large graphs using stochastic block models

“…Finding those structures can be beneficial in many fields, such as finding protein complexes in biological networks and topical, disciplinary groups in collaborative networks, etc [1,2,3,4,5,6,7].…”

Formula partitioning revisited

“…Amir and McIlraith used a graph representation similar to the primal hypergraph, and searched for a vertex separator in it [1]. The community structure (i.e., a decomposition into highly connected parts with few connections among them) of SAT formulae has also been investigated [2].…”