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Upper Bound on the Satisfiability Threshold of Regular Random (k,s)-SAT Problem

2016
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International Journal of Innovative Computing, Information and Control
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We consider a strictly regular random (k, s)-SAT problem and propose a GSRR model for generating its instances. By applying the first moment method and the asymptotic approximation of the γth coefficient for generating function f (z) λ , where λ and γ are growing at a fixed rate, we obtain a new upper bound 2 k log 2 − (k + 1) log 2/2 + ϵ k for this problem, which is below the best current known upper bound 2 k log 2 + ϵ k . Furthermore, it is also below the asymptotic bound of the uniform

doi:10.24507/ijicic.12.02.477
fatcat:cjpi7ckokbdarkgqrwp7gq7rum