Gate circuits in the algebra of transients

Brzozowski, Janusz; Gheorghiu, Mihaela

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 39 (2005) no. 1, pp. 67-91.

We study simulation of gate circuits in the infinite algebra of transients recently introduced by Brzozowski and Ésik. A transient is a word consisting of alternating $0$s and $1$s; it represents a changing signal. In the algebra of transients, gates process transients instead of $0$s and $1$s. Simulation in this algebra is capable of counting signal changes and detecting hazards. We study two simulation algorithms: a general one that works with any initial state, and a special one that applies only if the initial state is stable. We show that the two algorithms agree in the stable case. We also show that the general algorithm is insensitive to the removal of state variables that are not feedback variables. We prove the sufficiency of simulation: all signal changes occurring in binary analysis are predicted by the general algorithm. Finally, we show that simulation can be more pessimistic than binary analysis, if wire delays are not taken into account. We propose a circuit model that we conjecture to be sufficient for proving the equivalence of simulation and binary analysis for feedback-free circuits.

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