# 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

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topBadr, 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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