Fine Hierarchy of Regular Omega-Languages

By applying descriptive set theory we get several facts on the fine structure of regular ω-languages considered by K.Wagner. We present quite different, shorter proofs for main his results and get new results. Our description of the fine structure is new, very clear and automata-free. We prove also a closure property of the fine structure under Boolean operations. Our results demonstrate deep interconnections between descriptive set theory and theory of ω-languages.

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

[2]  V. L. Selivanov.  Hierearchies of hyperarithmetical sets and functions , 1983 .

[3]  V. L. Selivanov.  Refined hierarchy of formulas , 1991 .

[4]  A. Louveau,et al.  Borel classes and closed games: Wadge-type and Hurewicz-type results , 1987 .

[5]  Robert van Wesep,et al.  Wadge Degrees and Projective Ordinals: The Cabal Seminar, Volume II: Wadge degrees and descriptive set theory , 1978 .

[6]  Victor L. Selivanov,et al.  Fine hierarchies and Boolean terms , 1995, Journal of Symbolic Logic.

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

[8]  TWO-WEEK Loan COpy,et al.  University of California , 1886, The American journal of dental science.

[9]  L. Staiger.  Research in the theory of Ω-languages , 1987 .

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

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

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

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

[14]  John R. Steel,et al.  Determinateness and the separation property , 1981, Journal of Symbolic Logic.

[15]  William W. Wadge,et al.  Reducibility and Determinateness on the Baire Space , 1982 .

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

[17]  J. R. Büchi,et al.  Solving sequential conditions by finite-state strategies , 1969 .

[18]  Victor L. Selivanov.  Two Refinements of the Polynomial Hierarcht , 1994, STACS.

[19]  Thomas Wilke,et al.  Computing the Wadge Degree, the Lifschitz Degree, and the Rabin Index of a Regular Language of Infinite Words in Polynomial Time , 1995, TAPSOFT.

[20]  V. L. Selivanov.  Fine hierarchy and definable index sets , 1991 .