Abstract
How to choose decision variables often determines the performance of SAT solvers. In state-of-the-art SAT solvers, Variable State Independent Decaying Sum (VSIDS) has been used as a standard technique in the decision process. In this study, we analyze the VSIDS from the point of view of PageRank and propose a technique for improving the VSIDS. While the VSIDS focuses on local search spaces, the PageRank values are based on the relative importance from a global point of view. From this fact, we utilize the PageRank values for controlling the VSIDS and improve the performances of representative SAT solvers, MiniSAT and Glucose.
Highlights
When a Boolean formula is given, the Boolean Satisfiability (SAT) problem asks whether an assignment of variables exists, which evaluates the formula as true
We investigated the relation between PageRank and Variable State Independent Decaying Sum (VSIDS) and applied the PageRank value to the VSIDS score
We found that variables with a high PageRank tend to be selected as decision variables
Summary
When a Boolean formula is given, the Boolean Satisfiability (SAT) problem asks whether an assignment of variables exists, which evaluates the formula as true. A formula is given in Conjunctive Normal Form (CNF). The solvers for this kind of problem are called SAT solvers. Many SAT solvers adopt the Davis-PutnamLogemann-Loveland (DPLL) algorithm (Davis et al, 1962), which is based on a backtrack search. During the last dozen years, various important methods have been proposed to improve the performance of DPLL, such as, Conflict-Driven-Clause-Learning (CDCL) to prevent reappearance of similar searches, restart (Gomes et al, 1998) instead of backtracking to start different search from the first beginning in order to avoid heavy-tail behavior, and Variable State Independent Decaying Sum (VSIDS) decision heuristic (Moskewicz et al, 2001) to determine the priority to select variables to be assigned. Many CDCL/VSIDS-based solvers give scores to prioritize a set of variables that appear in learnt clauses in order to fully utilize the obtained learnt clauses
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