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Hyper-minimizing minimized deterministic finite state automata

Published online by Cambridge University Press:  20 December 2007

Andrew Badr
3210 Acklen Ave., Nashville, TN 37212, USA;
Viliam Geffert
Department of Computer Science, P. J. Šafárik University, Jesenná 5, 04001 Košice, Slovakia;
Ian Shipman
Department of Mathematics, University of Chicago, 5734 S. University Ave., Chicago, IL 60637, USA;
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We present the first (polynomial-time) algorithm for reducing a given deterministic finite state automaton (DFA) into a hyper-minimized DFA, which may have fewer states than the classically minimized DFA. The price we pay is that the language recognized by the new machine can differ from the original on a finite number of inputs. These hyper-minimized automata are optimal, in the sense that every DFA with fewer states must disagree on infinitely many inputs. With small modifications, the construction works also for finite state transducers producing outputs. Within a class of finitely differing languages, the hyper-minimized automaton is not necessarily unique. There may exist several non-isomorphic machines using the minimum number of states, each accepting a separate language finitely-different from the original one. We will show that there are large structural similarities among all these smallest automata.

Research Article
© EDP Sciences, 2008

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