Extensions of asynchronous circuits and the delay problem. Part II: Spike-free extensions and the delay problem of the second kind

In Part I of this paper, a larger asynchronous circuit was regarded as successfully simulating a smaller one if the former was a “good extension” of the latter, and the adverse effects of the delays on the inter-element wires, i.e., the delay problem, was investigated from this viewpoint. A closer examination made here, however, reveals that a good extension is usually insufficient for a truly successful simulation, and that a larger circuit must be “spike-free” in addition to being good. Accordingly, the delay problem is reinvestigated from this new viewpoint. Also, some relationships are established between good and spike-free extensions. An important result is that a spike-free delay network incorporation having binary wires only is a good extension. Further it is shown that the mathemtical situation can be greatly simplified by additionally requiring that the extension be semimodular