Stable Production Rule Sets are Deterministic

Abstract

Production Rule Sets (PRS) are a digital event-based model for CMOS circuits; stable production rule sets are those in which in every execution, every enabled rule remains enabled until it is executed. It has been conjectured that stable production rule sets are determinstic, meaning in particular that they cannot implement arbiters, and that the sequence of values sent on any channel is independent of the execution. In this paper, we prove these facts rigorously, directly from first principles. We also propose improvements to PRS testing tools based on the resulting theory.