The phase transition in random Horn satisfiability and its algorithmic implications

Details The phase transition in random Horn satisfiability and its algorithmic implications The phase transition in random Horn satisfiability and its algorithmic implications

1999-12-01

arxiv.org/abs/cs/9912001v1

Computer Science

Data Structures and Algorithms

26 pages. Journal version of papers in AIM'98, SODA'99. Submitted to Random Structures and Algorithms

Scientific paper

Let c>0 be a constant, and $\Phi$ 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 $\lim_{n\goesto \infty} \PR ({$\Phi$ 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.

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