@MISC{Ghosh_onexponential, author = {Subhas Kumar Ghosh}, title = {On Exponential Time Algorithm for k-SAT}, year = {} }

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Abstract

Abstract. In this work we present and analyze a simple algorithm for finding satisfying assignments of k-CNF (Boolean formulae in conjunctive normal form with at most k literals per clause). Our work is motivated by a simple question: Are there any structural property of the k-CNF which could help us to understand if a formula accepts isolated assignment? And can we deterministically find such isolated assignment if formula has one? In this work we show such a property exists in almost all non-trivial k-CNF formula, and we call it rigidity of a clause. Informally, rigidity of a clause can be defined to be how well connected a clause is to other clauses having same literals. If we satisfy a rigid clause for most of its literals then some of the variables are forced to take fixed values. Since, we can force such property and still get a satisfiable assignment; we save some of the decision paths in the algorithm and reduce its time complexity. Our main lemma shows that the number of branches in a depth n decision tree for k-CNF will be at least 2 n−