The Power of Choice for Random Satisfiability

Varsha Dani; Josep Diaz; Thomas Hayes; Cristopher Moore

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arXiv · 1211.6997

The Power of Choice for Random Satisfiability

Varsha Dani·Josep Diaz·Thomas Hayes·Cristopher Moore

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Abstract

We consider Achlioptas processes for k-SAT formulas. We create a semi-random formula with n variables and m clauses, where each clause is a choice, made on-line, between two or more uniformly random clauses. Our goal is to delay the satisfiability/unsatisfiability transition, keeping the formula satisfiable up to densities m/n beyond the satisfiability threshold alpha_k for random k-SAT. We show that three choices suffice to raise the threshold for any k >= 3, and that two choices suffice for all 3 <= k <= 25. We also show that two choices suffice to lower the threshold for all k >= 3, making the formula unsatisfiable at a density below alpha_k.

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Varsha Dani, Josep Diaz, Thomas Hayes, Cristopher Moore. 2012-11-29. The Power of Choice for Random Satisfiability. https://arxiv.org/abs/1211.6997

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