We have previously applied our system to two problems which were approached by Koza
using his Genetic Programming paradigm [Koza 92]. What follows is a brief description of
both of these problems, and a third Symbolic Integration problem, each of which is summarised in a tableau style adopted from Koza. It should be noted here that we use operators and terminals with their meaning with respect to grammars [Whigham 96], and are distinct from Koza's terminals and operators. With the exception of the Trigonometric Identities problem, which used
a slightly modified BNF grammar definition the reasons for which are given below, each of these
problems used the same production rules. The production rules for <expr> are as given earlier. As this and subsequent rules
are the only ones that require a choice, they are the ones that will be evolved in each of the
three problems described.