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On the Synthesis of Finite-State Machines from Samples of Their Behavior

The Nerode realization technique for synthesizing finite-state machines from their associated right-invariant equivalence relations is modified to give a method for synthesizing machines from finite subsets of their input-output behavior. The synthesis procedure includes a parameter that one may adjust to obtain machines that represent the desired behavior with varying degrees of accuracy and that consequently have varying complexities. We discuss some of the uses of the method, including an application to a sequential learning problem.