Balanced K-SAT and Biased random K-SAT on trees

Sumedha; Supriya Krishnamurthy; Sharmistha Sahoo

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arXiv · 1212.1942

Balanced K-SAT and Biased random K-SAT on trees

Sumedha·Supriya Krishnamurthy·Sharmistha Sahoo

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Abstract

We study and solve some variations of the random K-satisfiability problem - balanced K-SAT and biased random K-SAT - on a regular tree, using techniques we have developed earlier(arXiv:1110.2065). In both these problems, as well as variations of these that we have looked at, we find that the SAT-UNSAT transition obtained on the Bethe lattice matches the exact threshold for the same model on a random graph for K=2 and is very close to the numerical value obtained for K=3. For higher K it deviates from the numerical estimates of the solvability threshold on random graphs, but is very close to the dynamical 1-RSB threshold as obtained from the first non-trivial fixed point of the survey propagation algorithm.

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cond-mat.stat-mech cs.AI cs.CC

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Sumedha, Supriya Krishnamurthy, Sharmistha Sahoo. 2012-12-10. Balanced K-SAT and Biased random K-SAT on trees. https://arxiv.org/abs/1212.1942

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