The phase transition in random Horn satisfiability and its algorithmic implications
Abstract
Description
Let c>0 be a constant, and $Φ$ be a random Horn formula with n variables and $m=c\cdot 2^{n}$ 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 $\lim_{n\goesto \infty} \PR ({$Φ$ is satisfiable})= 1-F(e^{-c})$, where $F(x)=(1-x)(1-x^2)(1-x^4)(1-x^8)... $. Our method also yields as a byproduct an average-case analysis of this algorithm.
26 pages. Journal version of papers in AIM'98, SODA'99. Submitted to Random Structures and Algorithms
26 pages. Journal version of papers in AIM'98, SODA'99. Submitted to Random Structures and Algorithms