Convergence rates for the distribution of program outputs

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 for five computer models (any, average, cyclic, bit flip and Boolean). Mutation randomizes a genetic algorithm population in 1 4 (l + 1)(log(l) + 4) generations. Results for a genetic programming (GP) like model are confirmed by experiment.

The distribution of amorphous computer outputs

Fitness distributions (landscapes) of programs tend to a limit as they get bigger. Markov minorization gives upper bounds ((15.3 + 2.30m) / log I) on the length of program run on random or average computing devices. I is the size of the instruction set and m size of output register. Almost all programs are constants. Convergence is exponential with 90 % of programs of length 1.6 n2 N yielding constants (n = size input register and size of memory = N). This is supported by experiment. 1 The Amorphous or Average Computer In Computer Science we are used to the notion that computers are highly designed, precision engineered artifacts. Nevertheless we can theoretically analyse more amorphous computing devices. Indeed nanotechnology may be a route to their practical construction and use. Consider an abstract machine whose instruction set, rather than being designed, is chosen at random. We can consider random linear computer programs as Markov processes which move the computer from one state to another [1]. 1.1 Convergence of Outputs We start by considering what happens when a single instruction is executed. Then consider two consecutive instructions, then a program of a instructions and so on

Automated DNA Motif Discovery

Ensembl's human non-coding and protein coding genes are used to automatically find DNA pattern motifs. The Backus-Naur form (BNF) grammar for regular expressions (RE) is used by genetic programming to ensure the generated strings are legal. The evolved motif suggests the presence of Thymine followed by one or more Adenines etc. early in transcripts indicate a non-protein coding gene. Keywords: pseudogene, short and microRNAs, non-coding transcripts, systems biology, machine learning, Bioinformatics, motif, regular expression, strongly typed genetic programming, context-free grammar.Comment: 12 pages, 2 figure