 Thus formula_48 is a random variable representing what formula_49 has evolved to after formula_50 "generations".Let formula_51 be a class of functions, formula_52 be a class of representations, and formula_53 a class of distributions on formula_54.We say that formula_51 is "evolvable by formula_52 over formula_53" if there exists polynomials formula_58, formula_59, formula_60, and formula_61 such that for all formula_3 and all formula_63, for all ideal functions formula_4 and representations formula_45, with probability at least formula_66,
where the sizes of neighborhoods formula_14 for formula_69 are at most formula_70, the sample size is formula_71, the tolerance is formula_72, and the generation size is formula_73.