The Wadge Hierarchy of Deterministic Tree Languages

We provide a complete description of the Wadge hierarchy for deterministically recognizable 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 to the case of trees

[1]  Klaus W. Wagner,et al.  On omega-Regular Sets , 1979, Inf. Control..

[2]  Igor Walukiewicz,et al.  Deciding Nondeterministic Hierarchy of Deterministic Tree Automata , 2005, Electron. Notes Theor. Comput. Sci..

[3]  Damian Niwinski.  On Fixed-Point Clones (Extended Abstract) , 1986, ICALP.

[4]  Jean-Eric Pin,et al.  Infinite words - automata, semigroups, logic and games , 2004, Pure and applied mathematics series.

[5]  Filip Murlak.  On Deciding Topological Classes of Deterministic Tree Languages , 2005, CSL.

[6]  Jerzy Skurczynski.  The Borel Hierarchy is Infinite in the Class of Regular Sets of Trees , 1993, Theor. Comput. Sci..

[7]  Orna Kupferman,et al.  Relating word and tree automata , 1996, Proceedings 11th Annual IEEE Symposium on Logic in Computer Science.

[8]  Jacques Duparc,et al.  A hierarchy of deterministic context-free omega-languages , 2003, Theor. Comput. Sci..

[9]  Igor Walukiewicz,et al.  Relating Hierarchies of Word and Tree Automata , 1998, STACS.

[10]  Olivier Finkel,et al.  Wadge hierarchy of omega context-free languages , 2001, Theor. Comput. Sci..

[11]  Olivier Finkel,et al.  Borel ranks and Wadge degrees of context free $\omega$-languages , 2006, Mathematical Structures in Computer Science.

[12]  Igor Walukiewicz,et al.  A gap property of deterministic tree languages , 2003, Theor. Comput. Sci..

[13]  Tomasz Fryderyk Urbanski.  On Deciding if Deterministic Rabin Language Is in Büchi Class , 2000, ICALP.

[14]  Victor L. Selivanov.  Wadge Degrees of [omega]-Languages of Deterministic Turing Machines , 2003, RAIRO Theor. Informatics Appl..

[15]  Olivier Finkel,et al.  Borel hierarchy and omega context free languages , 2003, Theor. Comput. Sci..

[16]  A. Kechris.  Classical descriptive set theory , 1987 .

[17]  Klaus W. Wagner.  Eine topologische Charakterisierung einiger Klassen regulärer Folgenmengen , 1977, J. Inf. Process. Cybern..