The decision and synthesis problems in semimodular switching theory

This paper presents an extension of the Muller-Bartky theory of asynchronous switching circuits. A circuit specification is a set of vectors whose components are non-negative integers and which satisfies certain other conditions. The j-th component of such a vector represents the number of times which the signal at the j-th node has changed since the circuit was started. The principal result of the paper characterizes the class of circuit specifications which may be realized by semimodular switching circuits. An alternative method of circuit specification is defined and shown to be equivalent.