Why Simulation-Based Approachs with Combined Fitness are a Good Approach for Mining Spaces of Turing-equivalent Functions

We show negative results about the automatic generation of programs within bounded-time. Combining recursion theory and statistics, we contrast these negative results with positive computability results for iterative approachs like genetic programming, provided that the fitness combines e.g. fastness and size. We then show that simulation-based approachs (approachs evaluating only by simulation the quality of programs) like GP are not too far from the minimal time required for evaluating these combined fitnesses.