Minimization and Synthesis of the Tail inSequential Compositions of Mealy Machines

We consider a system consisting of a sequential composition of Mealy machines, called head and tail. We study two problems related to these systems. First, models of both head and tail components are available, and the aim is to obtain a replacement for the tail with the minimum number of states. We introduce a minimization method for this context which yields an exponential improvement over the state of the art. In the second problem, only the head is known and a desired model for the whole system is given. The objective is to construct a tail that causes the system to behave according to the given model. We give a polynomial time algorithm that computes whether such a tail exists, whereas methods developed for general unknown component equations take exponential time. However, we also show that there are instances of the problem where the size of the tail is bounded from bellow by an exponential function in the sizes of the head and the desired system. This shows that the complexity of the synthesis procedure is at least exponential, matching the upper bound in complexity provided by the existing methods. 2012 ACM Subject Classification Hardware → Circuit optimization

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