ANALYSIS OF BILLIARD BALL COMPUTATION USING PHASE-SPACE LOGICS

When analyzing individual gates in circuitry, one usually assumes that inputs are either 0 or 1, as are the outputs, but the fact is that th ese input values are really either ''high'' voltage or ''low'' voltage . Determining whether or not a given input is to be considered as high or low depends on a physical measurement of the voltage. Since physic al measurement is never exact, it is more realistic to consider ''high ,'' ''low,'' and ''indeterminate,'' hence considering three possible v alues, rather than two, when reasoning about computer hardware. When c onsidering physical measurement as part of the determination as to wha t inputs and outputs are for a given gate, one can no longer reason ab out these gates using boolean logic. There are several possible non-bo olean alternatives one may consider. We will examine motivation for so me such alternatives and point out how we might apply them to a partic ular model of computation: the billiard ball model. (C) 1998 Elsevier Science B.V. All rights reserved.