Abstract program evaluation and its application to sorter evolution

This paper introduces abstract program evaluation (APE) that, for certain kinds of evolutionary induction problems, abstractly captures the maximal set of a problem's fitness tests. Abstraction of test cases can substantially reduce the number of such cases-fewer test cases lead to faster fitness computation, APE thereby can make some heretofore untenable induction problems solvable. Furthermore, since the computational representation (program, circuit, etc.) being evolved with APE is abstractly tested on every possible input, evolved solutions which pass all abstract tests are general-APE guarantees correctness for every possible input. APE transforms operators in the representation to compute with the abstract values of the abstract test cases instead of with concrete values (i.e., integers or reals); it is a form of symbolic evaluation of the executable representation. The paper discusses induction problems to which APE is suited as well as its limitations.