Resumen de Finiteness properties of some families of GP-trees

César Luis Alonso González , José Luis Montaña Arnaiz

• We provide upper bounds for the Vapnik-Chervonenkis dimension of classes of subsets of IRn that can be recognized by computer programs built from arithmetical assignments, infinitely differentiable algebraic operations (like k-root extraction and, more generally, operations defined by algebraic series of fractional powers), conditional statements and while instructions. This includes certain classes of GP-trees considered in Genetic Programming for symbolic regression and bi-classification. As a consequence we show explicit quantitative properties that can help to design the fitness function of a GP learning machine.