On the Continuity Set of an omega Rational Function

Olivier Carton (1) , Olivier Finkel (2) , Pierre Simonnet (3)

1 LIAFA - Laboratoire d'informatique Algorithmique : Fondements et Applications
2 LIP - Laboratoire de l'Informatique du Parallélisme
3 SPE - Sciences pour l'environnement

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 Pi^0_2-subset of X^omega for some alphabet X is the continuity set C(F) of an omega-rational synchronous function F defined on X^omega.

Keywords: Infinitary rational relations; Omega rational functions; Topology; Points of continuity; Decision problems; Omega rational languages; Omega context-free languages

Domains: Computer Science [cs]; Computational Complexity [cs.CC]; Computer Science [cs]; Logic in Computer Science [cs.LO]

Olivier Carton, Olivier Finkel, Pierre Simonnet. On the Continuity Set of an omega Rational Function. RAIRO - Theoretical Informatics and Applications (RAIRO: ITA), 2008, 42 ((1)), pp.183-196. ⟨ensl-00216624⟩