The phase transition in random horn satisfiability and its algorithmic implications

Authors:
Gabriel Istrate
Affiliations:
D-2 Division, Los Alamos National Laboratory, Mail Stop M 997, Los Alamos, NM
Venue:
Random Structures & Algorithms
Year:
2002

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Abstract

Let c 0 be a constant, and Φ be a random Horn formula with n variables and m = c . 2n clauses, chosen uniformly at random (with repetition) from the set of all nonempty Horn clauses in the given variables. By analyzing PUR, a natural implementation of positive unit resolution, we show that limn→∞ Pr(Φ is satisfiable) = 1 - F(e-c), where F(x) = (1 - x)(1 - x2)(1 - x4) (1 - x8) .... Our method also yields as a byproduct an average-case analysis of this algorithm.