The Wadge-Wagner Hierarchy of omega-Rational Sets

We present a unified treatment of the hierarchy defined, by Klaus Wagner for omega-rational sets and also introduced in the more general framework of descriptive set theory by William W. Wadge. We show that this hierarchy can be defined by syntactic invariants, using the concept of an omega-semigroup.

[1]  Wolfgang Thomas,et al.  Automata on Infinite Objects , 1991, Handbook of Theoretical Computer Science, Volume B: Formal Models and Sematics.

[2]  J. Howie.  Fundamentals of semigroup theory , 1995 .

[3]  Pierre Simonnet.  Automates et theorie descriptive , 1992 .

[4]  Robert K. Brayton,et al.  Structural Complexity of Omega-Automata , 1995, STACS.

[5]  Thomas Wilke.  An Eilenberg Theorem for Infinity-Languages , 1991, ICALP.

[6]  Douglas Lind,et al.  An Introduction to Symbolic Dynamics and Coding , 1995 .

[7]  Olivier Carton,et al.  Chains and Superchains for ω-Rational Sets, Automata and Semigroups , 1997, Int. J. Algebra Comput..

[8]  Ludwig Staiger,et al.  Automatentheoretische und automatenfreie Charakterisierungen topologischer Klassen regulärer Folgenmengen , 1974, J. Inf. Process. Cybern..

[9]  Olivier Carton.  Mots infinis, w-semigroupes et topologie , 1993 .

[10]  Thomas Wilke,et al.  Computing the Rabin Index of a Regular Language of Infinite Words , 1996, Inf. Comput..

[11]  Rana Barua.  The Hausdorff-Kuratowski Hierarchy of omega-Regular Languages and a Hierarchy of Muller Automata , 1992, Theor. Comput. Sci..

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

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

[14]  Thomas Wilke,et al.  An Algebraic Theory for Regular Languages of Finite and Infinite Words , 1993, Int. J. Algebra Comput..

[15]  Nicolas Bedon.  Automata, Semigroups and Recognizability of Words on Ordinals , 1998, Int. J. Algebra Comput..

[16]  Jorge Almeida,et al.  Finite Semigroups and Universal Algebra , 1995 .

[17]  Zohar Manna,et al.  A hierarchy of temporal properties (invited paper, 1989) , 1990, PODC '90.

[18]  Michael Kaminski.  A Classification of omega-Regular Languages , 1985, Theor. Comput. Sci..

[19]  A. Louveau,et al.  Some results in the wadge hierarchy of borel sets , 1983 .