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 mathematically and experimentally. It is mathematically proven that the average number of answer sets for a random program converges to a constant when the number of atoms is sufficiently large. 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 large
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