Topological Complexity of Context-Free omega-Languages: A Survey

Olivier Finkel (1, 2, 3)

1 ELM - Équipe de Logique Mathématique
2 IMJ - Institut de Mathématiques de Jussieu
3 LIP - Laboratoire de l'Informatique du Parallélisme

We survey recent results on the topological complexity of context-free omega-languages which form the second level of the Chomsky hierarchy of languages of infinite words. In particular, we consider the Borel hierarchy and the Wadge hierarchy of non-deterministic or deterministic context-free omega-languages. We study also decision problems, the links with the notions of ambiguity and of degrees of ambiguity, and the special case of omega-powers.

Keywords: topological complexity; Cantor topology; omega-powers; decision problems; Infinite words; pushdown automata; context-free omega-languages; decision problems.; complete sets; Borel hierarchy; Wadge hierarchy

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

Olivier Finkel. Topological Complexity of Context-Free omega-Languages: A Survey. Nachum Dershowitz and Ephraim Nissan. Language, Culture, Computation. Computing - Theory and Technology - Essays Dedicated to Yaacov Choueka on the Occasion of His 75th Birthday, Part I, 8001, Springer, pp.50--77, 2014, Lecture Notes in Computer Science, 978-3-642-45320-5. ⟨ensl-00286373v2⟩