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 these 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 physical measurement is never exact, it is more realistic to consider “high,” “low,” and “indeterminate,” hence considering three possible values, rather than two, when reasoning about computer hardware. When considering physical measurement as part of the determination as to what inputs and outputs are for a given gate, one can no longer reason about these gates using boolean logic. There are several possible non-boolean alternatives one may consider. We will examine motivation for some such alternatives and point out how we might apply them to a particular model of computation: the billiard ball model.
Physica D: Nonlinear Phenomena