Simulation of Gate Circuits with Feedback in Multi-Valued Algebras

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 and B, and is well understood. It has been generalized to an infinite algebra C and finite algebras Ck, k ≥ 2, where C2 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 in finite algebras Ck. 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 Ck, 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 Ck never appear. This permits ...

• Type: Conference
• Year: 2007
• Where: ISMVL
• Authors: Janusz A. Brzozowski, Yuli Ye
• Keywords: Artificial Intelligence, Gate Circuits, ISMVL 2007, Simulation, Ternary Algebra