For systems of interacting finite state machines (FSM's), manual designs sometimes use information derived from the other components to optimize one of them. An associated problem is to find the set of permissible sequential functionalities that can be implemented at a component while preserving the behavior of the total system. Most conventional approaches attempt to find such a set using th notion of don't care sequences, but in general, the complete set of permissible finite state machines are difficult to compute. As a result, only small subsets are derived and used in designing interacting components. However, there is no knowledge of how much optimality is lost using these subsets. This paper proposes a method for computing and representing the complete set of permissible finite state machines. We show that the complete set can be computed and represented by a single non-deterministic finite state machine, called the E-machine. The computation is different from any based on don't care sequences. The transition relation of the E-machine is obtained by a fixed point computation. The procedure has been implemented and initial experimental results are given.




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