Inference of Finite Automata Using Homing Sequences

We present new algorithms for inferring an unknown finite-state automaton from its input/output behavior in the absence of a means of r e ~ r t t i n p the machine to a start d a t e . A key technique used is inference of a homing sequence for the unknown automaton. Our infknrnce procedufes experiment with the unknown machine, and from time t o time require a teacher to supply counterexamplea to incorrect conjectures about the structure of the unknown automaton. In this setting, we describe a learning algorithm which, with probability 1 6, outputs a correct deecription of the unknown machine in time polynomial in the automaton's size, the length of the longest counterexample, and log(ll6). We present an analogous algorithm which makes use of a diversitybased representation of the finite-state system. Our algorithms are the first which are provably eflecfive for these problems, in the absence o j Q "reset." We also present probabilistic algorithms for permutation automata which do not require a teacher t o supply counterexamples. For inferring a permutation automaton of diversity D, we improve the best previous time bound by roughly a factor of D3 / log D.