Inference of finite automata using homing sequences

We present new algorithms for inferring an unknown finite-state automaton from its input/output behavior <italic>in the absence of a means of resetting the machine to a start state</italic>. A key technique used is inference of a <italic>homing sequence</italic> for the unknown automaton. Our inference procedures experiment with the unknown machine, and from time to time require a teacher to supply counterexamples to incorrect conjectures about the structure of the unknown automaton. In this setting, we describe a learning algorithm which, with probability 1-δ, outputs a correct description of the unknown machine in time polynomial in the automaton's size, the length of the longest counterexample, and log (1/<italic>δ</italic>). We present an analogous algorithm which makes use of a diversity-based representation of the finite-state system. <italic>Our algorithms are the first which are provably effective for these problems, in the absence of a “reset.”</italic> We also present probabilistic algorithms for permutation automata which do not require a teacher to supply counterexamples. For inferring a permutation automaton of diversity <italic>D</italic>, we improve the best previous time bound by roughly a factor of <italic>D</italic><supscrpt>3</supscrpt>/log<italic>D</italic>.

[1]  E. Mark Gold,et al.  System identification via state characterization , 1972 .

[2]  E. Mark Gold,et al.  Complexity of Automaton Identification from Given Data , 1978, Inf. Control..

[3]  DANA ANGLUIN,et al.  On the Complexity of Minimum Inference of Regular Sets , 1978, Inf. Control..

[4]  Dana Angluin,et al.  A Note on the Number of Queries Needed to Identify Regular Languages , 1981, Inf. Control..

[5]  Stewart W. Wilson.  Knowledge Growth in an Artificial Animal , 1985, ICGA.

[6]  G. Drescher.  Genetic AI: Translating piaget into lisp , 1986 .

[7]  Ronald L. Rivest,et al.  Diversity-based inference of finite automata , 1994, 28th Annual Symposium on Foundations of Computer Science (sfcs 1987).

[8]  Dana Angluin,et al.  Learning Regular Sets from Queries and Counterexamples , 1987, Inf. Comput..

[9]  Leonard Pitt,et al.  Reductions among prediction problems: on the difficulty of predicting automata , 1988, [1988] Proceedings. Structure in Complexity Theory Third Annual Conference.

[10]  M. Kearns,et al.  Crytographic limitations on learning Boolean formulae and finite automata , 1989, STOC '89.

[11]  Benjamin J. Kuipers,et al.  A Robust, Qualitative Approach To A Spatial Learning Mobile Robot , 1989, Optics East.

[12]  Leonard Pitt,et al.  Inductive Inference, DFAs, and Computational Complexity , 1989, AII.

[13]  Leonard Pitt,et al.  The minimum consistent DFA problem cannot be approximated within and polynomial , 1989, STOC '89.

[14]  Edward A. Feigenbaum,et al.  Switching and Finite Automata Theory: Computer Science Series , 1990 .

[15]  Maja J. Matarić,et al.  A Distributed Model for Mobile Robot Environment-Learning and Navigation , 1990 .

[16]  Robert E. Schapire,et al.  A new approach to unsupervised learning in deterministic environments , 1990 .

[17]  Leonard Pitt,et al.  Prediction-Preserving Reducibility , 1990, J. Comput. Syst. Sci..