Improving Propositional Satisfiability Algorithms by Dynamic Selection of Branching Rules

The problem of proving that a propositional boolean formula is satisfiable (SAT) is one of the fundamental problems in computer science. The most popular SAT algorithms are based on the well known Davis-Putnam procedure. There, to guide search, a branching rule is applied for selecting still unassigned variables and computing an assignment to this variable. Additionally, conflict analysis methods were developed which result in non-chronological backtracking that preserves the SAT algorithm to search nonrelevant parts of the search space. In this paper we focus on the impact of different branching rules and present an approach which (1) allows several and not only one branching rules to be applied and (2) uses informationen from non-chronological backtracking to dynamically adapt the probabilities of the branching rules to be selected. Our approach results in a faster and more robust behaviour of the SAT algorithm, whereby speedups of up to 185% can be achieved.