Selection of search strategies for solving 3-SAT problems

Abstract

The paper concerns the problem of Boolean satisfiability checking, which is recognized as one of the most important issues in the field of modern digital electronic system verification and design. The paper analyzes different strategies and scenarios of the proving process, and presents a modified and extended version of the author's FUDASAT algorithm. The original FUDASAT methodology is an intuitive approach that employs a commonsense reasoning methodology. The main objective of the work is to investigate the SAT-solving process and try to formulate a set of rules controlling the reasoning process of the FUDASAT inference engine. In comparison with the author's previous works, the paper introduces new mechanisms: hypergraph analysis, multiple variable assignments and search space pruning algorithms. The approach considers only 3-SAT class functions, although a generalization of the method is discussed as well. The presented approach has been tested on various benchmarks and compared with the original pure FUDASAT algorithm as well as with other algorithms known from the literature. Finally, the benefits of the proposed SAT solving technique are summarized.

Introducing fuzzy default logic into WalkSAT algorithm

“…Recently very popular in the field are techniques based on various heuristics [9][10][11][12]. As a matter of fact, we need to find the information about relationship between variables hidden within the function.…”

“…The previous works of the first author concerning SAT solving problems [12] pointed out parallel relationship between SAT solving and non-monotonic reasoning [6]. FDL formalism defined in [6] is based on such non-standard inference scheme that allows invalidating some hypotheses during the inference process.…”

“…Recently, the author has proposed two algorithms of pruning searching space (PSS) [12] that allow limiting the number of investigated possible solutions. Both algorithms are based on a cliques analysis.…”

“…FUDASAT system published in [12] was based on the direct implementation of this technique into the inference 978-1-4799-7009-4/14/$31.00 ©2014 IEEE process. Moreover that application introduced dynamic FDR rules, while the approach presented in this paper focuses on the implementation of FDL mechanism in the WalkSAT procedure during the variable flipping process.…”

“…SAT solving techniques are also used in formulating many combinatorial and logical problems and they allow verifying the correctness of formal models. Since the announcement of the first SAT-solving algorithm DP [1] in 1960, many researchers have proposed various approaches to the problem [2][3][4][8][9][10][11][12]. Moreover, the SAT-Solving community constantly grows and different techniques can be compared on huge number of benchmarks [13].…”