The Wadge Hierarchy of Max-Regular Languages

Recently, Mikołaj Boja´nczyk introduced a class of max-regular languages, an extension of regular languages of infinite words preserving many of its usual properties. This new class can be seen as a different way of generalizing the notion of regularity from finite to infinite words. This paper compares regular and max-regular languages in terms of topological complexity. It is proved that up to Wadge equivalence the classes coincide. Moreover, when restricted to ∆0 2-languages, the classes contain virtually the same languages. On the other hand, separating examples of arbitrary complexity exceeding ∆0 2 are constructed.

• Type: Conference
• Year: 2009
• Where: FSTTCS
• Authors: Jérémie Cabessa, Jacques Duparc, Alessandro Facchini, Filip Murlak
• Keywords: FSTTCS 2009, Infinite Words, Max-regular Languages, Theoretical Computer Science, Usual Properties