Simulation of Gate Circuits with Feedback in Multi-Valued Algebras

Abstract

Simulation of gate circuits is an efficient method of detecting hazards and oscillations that may occur because of delays. Ternary simulation consists of two algorithms, A andB, and is well understood. It has been generalized to an infinite algebra C and finite algebras Ckappa, k ges 2, where Ci is ternary algebra. Simulation in C has been studied extensively for feedback-free circuits, for which algorithm A always terminates and algorithm B is unnecessary. We study the simulation of gate circuits with feedback infinite algebras Ckappa- The gate functions are restricted to a set that includes all the 1- and 2-variable functions and multi-input AND, OR, NAND, NOR, XOR and XNOR functions. We prove that Algorithm B in Algebra Ckappa, for k > 2, provides no more information than in ternary algebra. Thus, for any gate in any circuit, the final result of Algorithm B is always one of the binary values, 0 or 1, or the "uncertain" value; the remaining values of Ckappa never appear. This permits us to replace Algorithm B in Ckappa by the same algorithm in ternary algebra, and to reduce the simulation time.