Abstract
The height of the Wadge Hierarchy for the Alternation Free Fragment of μ-calculus is known to be at least ε 0. It was conjectured that the height is exactly ε 0. We make a first step towards the proof of this conjecture by showing that there is no \(\Delta^\mu_{2}\) definable set in between the levels ω ω and ω 1 of the Wadge Hierarchy of Borel Sets.
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References
Arnold, A., Niwinski, D.: Rudiments of μ-Calculus. Studies in Logic, vol. 146. Elsevier, Amsterdam (2001)
Berwanger, D., Grädel, E., Lenzi, G.: The variable hierarchy of the μ-calculus is strict. Theory of Computing Systems 40, 437–466 (2007)
Duparc, J.: Hierarchy and Veblen Hierarchy Part 1: Borel Sets of Finite Rank. Journal of Symbolic Logic 66(1), 56–86 (2001)
Duparc, J.: A Hierarchy of Deterministic Context-Free ω-languages. Theoretical Computer Science 290, 1253–1300 (2003)
Duparc, J., Facchini, A.: Describing the Wadge Hierarchy for the Alternation Free Fragment of μ-Calculus (I) - The Levels Below ω 1. Draft version, http://www.hec.unil.ch/logique/recherche/travaux/
Duparc, J., Murlak, F.: On the Topological Complexity of Weakly Recognizable Tree Languages. In: Csuhaj-Varjú, E., Ésik, Z. (eds.) FCT 2007. LNCS, vol. 4639, pp. 261–273. Springer, Heidelberg (2007)
Emerson, E.A., Jutla, C.S.: Tree Automata, μ-Calculus and Determinacy (Extended Abstract). In: FOCS 1991, pp. 368–377 (1991)
Streett, R.S., Emerson, E.A.: An automata theoretic decision procedure for the propositional μ-calculus. Information and Computation 81(3), 249–264 (1989)
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Duparc, J., Facchini, A. (2008). Describing the Wadge Hierarchy for the Alternation Free Fragment of μ-Calculus (I). In: Beckmann, A., Dimitracopoulos, C., Löwe, B. (eds) Logic and Theory of Algorithms. CiE 2008. Lecture Notes in Computer Science, vol 5028. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-69407-6_22
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DOI: https://doi.org/10.1007/978-3-540-69407-6_22
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-69405-2
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