Simulation of gate circuits in the algebra of transients

Authors:
Janusz Brzozowski;Mihaela Gheorghiu
Affiliations:
School of Computer Science, University of Waterloo, Waterloo, ON, Canada;School of Computer Science, University of Waterloo, Waterloo, ON, Canada
Venue:
CIAA'02 Proceedings of the 7th international conference on Implementation and application of automata
Year:
2002

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Abstract

We study simulation of gate circuits in algebra C recently introduced by Brzozowski and Ésik. A transient is a word consisting of alternating 0s and 1s; it represents a changing signal. In C, gates process transients instead of 0s and 1s. Simulation in C is capable of counting signal changes, and detecting hazards. We study two simulation algorithms: a general one, A, that works with any state, and Ã, that applies if the initial state is stable. We show that the two algorithms agree in the stable case. We prove the sufficiency of the simulation: all signal changes occurring in binary analysis are also predicted by Algorithm A.