By Janusz A. Brzozowski
In fresh years, there was an exceptional surge of curiosity in asynchronous circuits, principally during the improvement of latest asynchronous layout methodologies. This e-book presents a complete concept of asynchronous circuits, together with modelling, research, simulation, specification, verification, and an advent to their layout.
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Extra info for Asynchronous Circuits (Monographs in Computer Science)
Recall that we are assuming that the input and the output of the delay component have the same value initially and that the signals are binary. Under these special circumstances, we may represent the input waveform as a (finite or infinite) sequence (tl, t2"") of increasing real numbers, where each real number ti represents an instant at which the input signal changes. 5,13), together with the initial value O. In a similar way, we represent the output waveform of a delay component by the sequence (t~, t;, ...
Y;: VIWI --+ V. This is the Boolean function of the gate corresponding to the gate vertex. For a wire vertex Zi, the vertex function Zi, Zi: VII I+191 --+ V, provides the value of the inputdelay or gate vertex connected to the incoming edge of the wire vertex. For an input-delay vertex Xi, the vertex function is Xi. For an input vertex, the vertex function maps a state of the environment to the vertex domain V. This function is called Xi. We may think of Xi as the input value provided by the environment; how the environment determines this value is of no interest to us.
1. Digraph G. A walk is a sequence of edges (el, ... , the head of ei is the same as the tail of ei+1, for all i = 1, ... ,p - l. The number p of edges in a walk is its length. A walk can also be uniquely specified by the sequence Vo, ... , vp of vertices encountered during the walk. If the edges of a walk are all distinct, it is called a trail. For example, the vertex sequence (1,2,3,1,3,1) in G, which describes a walk of length 5, is not a trail because the edge (3,1) appears twice. If all the vertices of a walk, except possibly the first and the last, are distinct, it is called a path.