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Hyper-minimizing minimized deterministic finite state automata

Published online by Cambridge University Press:  20 December 2007

Andrew Badr ,
Viliam Geffert  and
Ian Shipman
Andrew Badr
Affiliation:
3210 Acklen Ave., Nashville, TN 37212, USA; badr@uiuc.edu
Viliam Geffert
Affiliation:
Department of Computer Science, P. J. Šafárik University, Jesenná 5, 04001 Košice, Slovakia; viliam.geffert@upjs.sk
Ian Shipman
Affiliation:
Department of Mathematics, University of Chicago, 5734 S. University Ave., Chicago, IL 60637, USA; ics@math.uchicago.edu
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Abstract

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.

Keywords

Finite state automataregular languages.
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 43 , Issue 1 , January 2009 , pp. 69 - 94
Copyright
© EDP Sciences, 2008

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