Hyper-minimizing minimized deterministic finite state automata

Andrew Badr; Viliam Geffert; Ian Shipman

RAIRO - Theoretical Informatics and Applications (2007)

  • Volume: 43, Issue: 1, page 69-94
  • ISSN: 0988-3754

Abstract

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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.

How to cite

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Badr, Andrew, Geffert, Viliam, and Shipman, Ian. "Hyper-minimizing minimized deterministic finite state automata." RAIRO - Theoretical Informatics and Applications 43.1 (2007): 69-94. <http://eudml.org/doc/92908>.

@article{Badr2007,
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. },
author = {Badr, Andrew, Geffert, Viliam, Shipman, Ian},
journal = {RAIRO - Theoretical Informatics and Applications},
keywords = {Finite state automata; regular languages.; finite state automata; regular languages},
language = {eng},
month = {12},
number = {1},
pages = {69-94},
publisher = {EDP Sciences},
title = {Hyper-minimizing minimized deterministic finite state automata},
url = {http://eudml.org/doc/92908},
volume = {43},
year = {2007},
}

TY - JOUR
AU - Badr, Andrew
AU - Geffert, Viliam
AU - Shipman, Ian
TI - Hyper-minimizing minimized deterministic finite state automata
JO - RAIRO - Theoretical Informatics and Applications
DA - 2007/12//
PB - EDP Sciences
VL - 43
IS - 1
SP - 69
EP - 94
AB - 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.
LA - eng
KW - Finite state automata; regular languages.; finite state automata; regular languages
UR - http://eudml.org/doc/92908
ER -

References

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