## Diversity-based Inference of Finite Automata (1994)

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Venue: | Journal of ACM |

Citations: | 73 - 1 self |

### BibTeX

@ARTICLE{Rivest94diversity-basedinference,

author = {Ronald L. Rivest and Robert and E. Schapire},

title = {Diversity-based Inference of Finite Automata},

journal = {Journal of ACM},

year = {1994}

}

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### Abstract

Abstract. We present new procedures for inferring the structure of a finite-state automaton (FSA) from its input \ output behavior, using access to the automaton to perform experiments. Our procedures use a new representation for finite automata, based on the notion of equivalence between tesfs. We call the number of such equivalence classes the diLersL@of the automaton; the diversity may be as small as the logarithm of the number of states of the automaton. For the special class of pennatatton aatornata, we describe an inference procedure that runs in time polynomial in the diversity and log(l/6), where 8 is a given upper bound on the probability that our procedure returns an incorrect result. (Since our procedure uses randomization to perform experiments, there is a certain controllable chance that it will return an erroneous result.) We also discuss techniques for handling more general automata. We present evidence for the practical efficiency of our approach. For example, our procedure is able to infer the structure of an automaton based on Rubik’s Cube (which has approximately 10 lY states) in about 2 minutes on a DEC MicroVax. This automaton is many orders of magnitude larger than possible with previous techniques, which would require time proportional at least to the number of global states. (Note that in this example, only a small fraction (10-14, of the global