An algorithm for random signed 3-SAT with Intervals
Abstract
In signed k-SAT problems, one fixes a set M and a set 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 ∈ S", where S ∈ S, and x is one of n variables. For Interval-SAT (iSAT), M is an ordered set and 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 2.3, with high probability, our algorithm succeeds in finding an assignment of values to the variables satisfying the formula.
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