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 \citelangdon:2002:crlp for the outputs of five computer models (any, average, cyclic, bit flip and Boolean). Mutation randomises a genetic algorithm population in 0.25(l+1)(log(l)+4) generations. While \citelangdon:2002:foga considers convergence of functions. We restate the results 0.5N(log(m)+4) and O(N)-O(N^3/2) for a genetic programming (GP) like model