Exactly Learning Automata of Small Cover Time

We present algorithms for exactly learning unknown environments that can be described by deterministic finite automata. The learner performs a walk on the target automaton, where at each step it observes the output of the state it is at, and chooses a labeled edge to traverse to the next state. The learner has no means of a reset, and does not have access to a teacher that answers equivalence queries and gives the learner counterexamples to its hypotheses. We present two algorithms: The first is for the case in which the outputs observed by the learner are always correct, and the second is for the case in which the outputs might be corrupted by random noise. The running times of both algorithms are polynomial in the cover time of the underlying graph of the target automaton.

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