On the equivalence of asynchronous control structures

This paper is concerned with the problem of detecting when two asynchronous control systems are equivalent. The systems investigated in the paper are first represented by means of a formal model called an asynchronous control structure (ACS). This model specifies the constraints imposed on the generation of control signals by a system by means of a simple graphical model called a marked graph. Behavioral equivalence is then characterized in terms of the set of all possible sequences of control signals that can be generated by the system. These sequences are represented by means of another (infinite) marked graph, called a behavior graph. Finally, it is shown that two control systems are equivalent if and only if their behavior graph representations have identical (finite) generating sets.