Preprint MCS-P387-1093 The Resonance Strategy*

x implies x. Even in algorithm writing and in circuit design, lemmas play a key role: minus(minus(x)) = in the former and NOT(AND(x,y)) = OR(NOT(x),NOT(y)) in the latter. Whether the object is to s prove a theorem, write an algorithm, or design a circuit, and whether the assignment is given to a per on or (preferably) to an automated reasoning program, the judicious use of lemmas often spells the e difference between success and failure. In this article, we focus on what might be thought of as a gen ralization of the concept of lemma, namely, the concept of resonator, and on a strategy, the resonance f e strategy, that keys on resonators. For example, where in Boolean groups—those in which the square o very x is the identity element e—the lemmas yzyz = e and yyzz = e are such that neither generalizes