On the continuity set of an Omega rational function

Olivier Carton; Olivier Finkel; Pierre Simonnet

RAIRO - Theoretical Informatics and Applications (2008)

  • Volume: 42, Issue: 1, page 183-196
  • ISSN: 0988-3754

Abstract

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In this paper, we study the continuity of rational functions realized by Büchi finite state transducers. It has been shown by Prieur that it can be decided whether such a function is continuous. We prove here that surprisingly, it cannot be decided whether such a function f has at least one point of continuity and that its continuity set C(f) cannot be computed. In the case of a synchronous rational function, we show that its continuity set is rational and that it can be computed. Furthermore we prove that any rational Π 2 0 -subset of Σω for some alphabet Σ is the continuity set C(f) of an ω-rational synchronous function f defined on Σω.

How to cite

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Carton, Olivier, Finkel, Olivier, and Simonnet, Pierre. "On the continuity set of an Omega rational function." RAIRO - Theoretical Informatics and Applications 42.1 (2008): 183-196. <http://eudml.org/doc/250351>.

@article{Carton2008,
abstract = { In this paper, we study the continuity of rational functions realized by Büchi finite state transducers. It has been shown by Prieur that it can be decided whether such a function is continuous. We prove here that surprisingly, it cannot be decided whether such a function f has at least one point of continuity and that its continuity set C(f) cannot be computed. In the case of a synchronous rational function, we show that its continuity set is rational and that it can be computed. Furthermore we prove that any rational $\{\bf \Pi\}^0_2$-subset of Σω for some alphabet Σ is the continuity set C(f) of an ω-rational synchronous function f defined on Σω. },
author = {Carton, Olivier, Finkel, Olivier, Simonnet, Pierre},
journal = {RAIRO - Theoretical Informatics and Applications},
keywords = {Infinitary rational relations; omega rational functions; topology; points of continuity; decision problems; omega rational languages; omega context-free languages.},
language = {eng},
month = {1},
number = {1},
pages = {183-196},
publisher = {EDP Sciences},
title = {On the continuity set of an Omega rational function},
url = {http://eudml.org/doc/250351},
volume = {42},
year = {2008},
}

TY - JOUR
AU - Carton, Olivier
AU - Finkel, Olivier
AU - Simonnet, Pierre
TI - On the continuity set of an Omega rational function
JO - RAIRO - Theoretical Informatics and Applications
DA - 2008/1//
PB - EDP Sciences
VL - 42
IS - 1
SP - 183
EP - 196
AB - In this paper, we study the continuity of rational functions realized by Büchi finite state transducers. It has been shown by Prieur that it can be decided whether such a function is continuous. We prove here that surprisingly, it cannot be decided whether such a function f has at least one point of continuity and that its continuity set C(f) cannot be computed. In the case of a synchronous rational function, we show that its continuity set is rational and that it can be computed. Furthermore we prove that any rational ${\bf \Pi}^0_2$-subset of Σω for some alphabet Σ is the continuity set C(f) of an ω-rational synchronous function f defined on Σω.
LA - eng
KW - Infinitary rational relations; omega rational functions; topology; points of continuity; decision problems; omega rational languages; omega context-free languages.
UR - http://eudml.org/doc/250351
ER -

References

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