2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/33336Let 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 AlgorithmsData Structures and AlgorithmsComputational ComplexityF.2.2;I.1.2;G.3text