Size of Random Programs to ensure Uniformity

Fitness distributions (landscapes) of programs tend to a limit as they get bigger. Markov chain convergence theorems give general upper bounds on the linear program sizes needed for convergence. Tight bounds (exponential in N , N log N and smaller) are given in [1] for the outputs of ve computer models (any, average, cyclic, bit ip and Boolean). Mutation randomises a genetic algorithm population in 4 (l + 1)(log(l) + 4) generations. While [2] considers convergence of functions. We restate the results 2 N(log(m) + 4) and O(N){O(N 3=2 ) for a genetic programming (GP) like model