Synchronous Composition of Quasi-Complete and Quasi-Deterministic FSMs

In this paper, we consider the synchronous composition of Finite State Machines (FSMs) that corresponds to instantaneous communication of hardware components. Such FSMs can be deterministic or nondeterministic, partial or complete. We first extend the existing synchronous composition operator from a pair of components to a collection of components with multiple input and output ports, and provide a procedure to compute the composition working directly on the collection of transition tables of the component FSMs. Then, based on the notion of input-output Moore pair (the output is not sensitive to the input), we prove the following sufficient condition: if the composition has the property that every cycle of ports has a component with a Moore pair, then the class of quasi-complete and quasi-deterministic FSMs is closed under the proposed synchronous composition.