Distance desert automata and the star height problem

Daniel Kirsten

RAIRO - Theoretical Informatics and Applications (2010)

  • Volume: 39, Issue: 3, page 455-509
  • ISSN: 0988-3754

Abstract

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We introduce the notion of nested distance desert automata as a joint generalization of distance automata and desert automata. We show that limitedness of nested distance desert automata is PSPACE-complete. As an application, we show that it is decidable in 22O(n) space whether the language accepted by an n-state non-deterministic automaton is of a star height less than a given integer h (concerning rational expressions with union, concatenation and iteration), which is the first ever complexity bound for the star height problem.

How to cite

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Kirsten, Daniel. "Distance desert automata and the star height problem." RAIRO - Theoretical Informatics and Applications 39.3 (2010): 455-509. <http://eudml.org/doc/92776>.

@article{Kirsten2010,
abstract = { We introduce the notion of nested distance desert automata as a joint generalization of distance automata and desert automata. We show that limitedness of nested distance desert automata is PSPACE-complete. As an application, we show that it is decidable in 22O(n) space whether the language accepted by an n-state non-deterministic automaton is of a star height less than a given integer h (concerning rational expressions with union, concatenation and iteration), which is the first ever complexity bound for the star height problem. },
author = {Kirsten, Daniel},
journal = {RAIRO - Theoretical Informatics and Applications},
keywords = {Recognizable languages; star height; distance automata.; recognizable languages; star heights; distance automata; desert automata; hierarchies; decidability; star height problem; free monoids},
language = {eng},
month = {3},
number = {3},
pages = {455-509},
publisher = {EDP Sciences},
title = {Distance desert automata and the star height problem},
url = {http://eudml.org/doc/92776},
volume = {39},
year = {2010},
}

TY - JOUR
AU - Kirsten, Daniel
TI - Distance desert automata and the star height problem
JO - RAIRO - Theoretical Informatics and Applications
DA - 2010/3//
PB - EDP Sciences
VL - 39
IS - 3
SP - 455
EP - 509
AB - We introduce the notion of nested distance desert automata as a joint generalization of distance automata and desert automata. We show that limitedness of nested distance desert automata is PSPACE-complete. As an application, we show that it is decidable in 22O(n) space whether the language accepted by an n-state non-deterministic automaton is of a star height less than a given integer h (concerning rational expressions with union, concatenation and iteration), which is the first ever complexity bound for the star height problem.
LA - eng
KW - Recognizable languages; star height; distance automata.; recognizable languages; star heights; distance automata; desert automata; hierarchies; decidability; star height problem; free monoids
UR - http://eudml.org/doc/92776
ER -

References

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