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Defining the speed independence of the Boolean asynchronous systems

A discrete time Boolean asynchronous system consists in a function Φ : {0, 1}n → {0, 1}n which iterates its coordinates Φ1, ..., Φn independently of each other. The durations of computation of Φ1, ..., Φn are supposed to be unknown. The analysis of such systems has as main challenge characterizing their dynamics in conditions of uncertainty. For this, a very cited classical paper is [1], where the fundamental concept of speed independence is introduced. The point is, like in most of these cases, that the engineers receive from such a work intuition, combined with a certain lack of rigor. Our aim is to try a mathematical reinforcement of the Muller’s theory of the asynchronous circuits, which should be a modest homage, over time, to its authors.
A list of models used in asynchronous systems theory is given in [3]. The mathematical tools used in this analysis may be found in [2].