Metastable operation is a fundamental phenomenon of sequential networks that process asynchronous inputs. Nevertheless, because of its subtle nature and the relatively low probability of its occurrence in conventional systems, this phenomenon is neither well understood nor widely appreciated. With continuing advances in digital technology, however, there is a growing interest in large-scale highly parallel systems. Such systems are likely to involve numerous high-frequency asynchronous interactions, which may result in frequent measures to prevent such failures. In recent years, a number of researchers have been working with some success to develop techniques for dealing with this failure mode. The purpose of this paper is to present a comprehensive theory of metastable operation that may lead to a better understanding of this phenomenon and provide theoretical support for further work in this area.

Synchronous sequential networks (SSN's) with high-frequency asynchronous inputs are subject to substantial failure rates due to the failure of input synchronizing networks. An apparent solution to this problem is to design asynchronous sequential networks (ASN's) to process the asynchronous inputs directly using the unrestricted input change technique of Unger. It is noted that this technique requires the use of inertial-delay elements and it is shown that inertial-delay elements can also be used to design reliable input synchronizers directly. Several common inertial-delay designs are examined. It is shown that none can be guaranteed reliable. An extensive dynamic analysis is required to prove the unreliability of one of these, an inertial delay which uses a Schmitt trigger. It is thus established that ASN's are subject to the same type of reliability problems as those recently exposed for synchronizers in synchronous networks. Furthermore, inertial delays are shown to be of central importance in that the development of a reliable inertial delay will solve both synchronous and asynchronous reliability problems.