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arXiv · 1105.2525

An algorithm for random signed 3-SAT with Intervals

Kathrin Ballerstein·Dirk Oliver Theis
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Abstract

In signed k-SAT problems, one fixes a set M and a set $\mathcal S$ of subsets of M, and is given a formula consisting of a disjunction of m clauses, each of which is a conjunction of k literals. Each literal is of the form "$x \in S$", where $S \in \mathcal S$, and x is one of n variables. For Interval-SAT (iSAT), M is an ordered set and $\mathcal S$ the set of intervals in M. We propose an algorithm for 3-iSAT, and analyze it on uniformly random formulas. The algorithm follows the Unit Clause paradigm, enhanced by a (very limited) backtracking option. Using Wormald's ODE method, we prove that, if $m/n \le 2.3$, with high probability, our algorithm succeeds in finding an assignment of values to the variables satisfying the formula.

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Kathrin Ballerstein, Dirk Oliver Theis. 2011-05-12. An algorithm for random signed 3-SAT with Intervals. https://arxiv.org/abs/1105.2525

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