Instruction and Solution Probabilities as Heuristics for Inductive Programming (2506.13804v1)

Abstract: Instruction subsets (ISs) are heuristics that can shrink the size of the inductive programming (IP) search space by tens of orders of magnitude. Here, we extend the IS approach by introducing instruction and solution probabilities as additional heuristics. Instruction probability reflects the expectation of an instruction occurring in a solution, based on the frequency of instruction occurrence in a large code sample. The solution probability for a partial or complete program is simply the product of all constituent instruction probabilities, including duplicates. We treat the minimum solution probabilities observed in code sample program units of different sizes as solution probability thresholds. These thresholds are used to prune the search space as partial solutions are constructed, thereby eliminating any branches containing unlikely combinations of instructions. The new approach has been evaluated using a large sample of human code. We tested two formulations of instruction probability: one based on instruction occurrence across the entire code sample and another that measured the distribution separately for each IS. Our results show that both variants produce substantial further reductions in the IP search space size of up to tens of orders of magnitude, depending on solution size. In combination with IS, reductions of over 100 orders of magnitude can be achieved. We also carried out cross-validation testing to show that the heuristics should work effectively with unseen code. The approach is described and the results and some ideas for future work are discussed.