Random Logic Programs: Linear Model

TL;DR

This paper introduces a linear model for generating sparse random logic programs and analyzes their statistical properties, including answer set counts and size distributions, with theoretical proofs and experimental validation.

Contribution

It presents the first linear model for random logic programs and provides mathematical analysis of their answer set properties, supported by experiments.

Findings

Average number of answer sets converges to a constant as atoms increase

Answer set size distribution tends to a normal distribution for large atom counts

Experimental results support the linear model's validity

Abstract

This paper proposes a model, the linear model, for randomly generating logic programs with low density of rules and investigates statistical properties of such random logic programs. It is mathematically shown that the average number of answer sets for a random program converges to a constant when the number of atoms approaches infinity. Several experimental results are also reported, which justify the suitability of the linear model. It is also experimentally shown that, under this model, the size distribution of answer sets for random programs tends to a normal distribution when the number of atoms is sufficiently large.