CSM-464: On the Limiting Distribution of Program Sizes in Tree-based Genetic Programming

We provide strong theoretical and experimental evidence that standard sub-tree crossover with uniform selection of crossover points pushes a population of a-ary GP trees towards a distribution of tree sizes of the form: [see document for formula] where n is the number of internal nodes in a tree and pa is a constant. This result generalises the result previously reported in [7, 10, 8, 9] for the case a = 1