A Formal Framwork for Evaluating Heuristic Programs

摘要

We address the question of how one evaluates the usefulness of a heuristic program on a particular input. If theoretical tools do not allow us to decide for every instance whether a particular heuristic is fast enough, might we at least write a simple, fast ocmpanion program that makes this decision on some inputs of interest? We call such a companion program a timer for the heuristic. Timers are related to program checkers, as defined by Blum[3], in the following sense: Checkers are companion programs that check the correctness of the output produced by programs on particular instances; timers, on the other hand, are companion programs that attempt to bound the running time on particular instances of correct programs whose running times have not been fully analyzed. This paper provides a family of definitions that formalize the notion of a timer and some preliminary results that demonstrate the utility of these definitions.