Abstract
We consider Achlioptas processes for k-SAT formulas. That is, we consider semi-random formulas with n variables and m = αn clauses, where each clause is a choice, made on-line, between two or more independent and uniformly random clauses. Our goal is to move the sat/unsat transition, making the density α = m/n at which these formulas become unsatisfiable larger or smaller than the satisfiability threshold α k for uniformly random k-SAT formulas. We show that three choices suffice to raise the threshold for any k ≥ 3, and that two choices suffice for 3 ≤ k ≤ 50. We also show that (assuming the threshold conjecture is true) two choices suffice to lower the threshold for all k ≥ 3, and that (unconditionally) a constant number of choices suffice.
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Dani, V., Diaz, J., Hayes, T., Moore, C. (2013). The Power of Choice for Random Satisfiability. In: Raghavendra, P., Raskhodnikova, S., Jansen, K., Rolim, J.D.P. (eds) Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques. APPROX RANDOM 2013 2013. Lecture Notes in Computer Science, vol 8096. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40328-6_34
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DOI: https://doi.org/10.1007/978-3-642-40328-6_34
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