The Wadge Hierarchy of Deterministic Tree Languages

The Wadge Hierarchy of Deterministic Tree Languages

We provide a complete description of the Wadge hierarchy for deterministically recognisable sets of infinite trees. In particular we give an elementary procedure to decide if one deterministic tree language is continuously reducible to another. This extends Wagner’s results on the hierarchy of ω-regular languages of words to the case of trees.

The Wadge Hierarchy of Max-Regular Languages

Recently, Mikołaj Bojańczyk 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 hierarchy of omega context-free languages

The main result of this paper is that the length of the Wadge hierarchy of omega context-free languages is greater than the Cantor ordinal 0, and the same result holds for the conciliating Wadge hierarchy, de1ned by Duparc (J. Symbolic Logic, to appear), of in1nitary context-free languages, studied by Beauquier (Ph.D. Thesis, Universit9 e Paris 7, 1984). In the course of our proof, we get resul...

The Wadge Hierarchy of Petri Nets ω-Languages

We describe the Wadge hierarchy of the ω-languages recognized by deterministic Petri nets. This is an extension of the celebrated Wagner hierarchy which turned out to be the Wadge hierarchy of the ω-regular languages. Petri nets are more powerful devices than finite automata. They may be defined as partially blind multi-counter automata. We show that the whole hierarchy has height ω 2 , and giv...

The Wadge Hierarchy of Petri Nets omega-Languages