Hostname: page-component-586b7cd67f-rdxmf Total loading time: 0 Render date: 2024-12-01T02:17:21.094Z Has data issue: false hasContentIssue false
  • English
  • Français

Wadge Degrees of ω-Languages of DeterministicTuring Machines

Published online by Cambridge University Press:  15 November 2003

Victor Selivanov
Victor Selivanov*
Affiliation:
Universität Siegen, Theoretische Informatik, Fachbereich 6, Germany; [email protected]. Novosibirsk State Pedagogical University Chair of Informatics and Discrete Mathematics, Russia; [email protected] .
Get access

Abstract

We describe Wadge degrees of ω-languages recognizable by deterministic Turing machines. In particular, it is shown that the ordinal corresponding to these degrees is ξω where ξ = ω1CK is the first non-recursive ordinal known as the Church–Kleene ordinal. This answers a question raised in [2].

Keywords

HierarchyWadge degreeω-languageordinalTuring machineset-theoretic operation.
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 37 , Issue 1 , January 2003 , pp. 67 - 83
Copyright
© EDP Sciences, 2003

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

A. Andretta, Notes on Descriptive Set Theory. Manuscript (2001).
Duparc, J., A hierarchy of deterministic context-free ω-languages. Theoret. Comput. Sci. 290 (2003) 1253-1300. CrossRef
Yu.L. Ershov, On a hierarchy of sets II. Algebra and Logic 7 (1968) 15-47 (Russian).
J. Köbler, U. Shöning and K.W. Wagner, The difference and truth-table hierarchies for NP, Preprint 7. Dep. of Informatics, Koblenz (1986).
K. Kuratowski and A. Mostowski, Set Theory. North Holland, Amsterdam (1967).
A. Louveau, Some results in the Wadge hierarchy of Borel sets. Springer, Lecture Notes in Math. 1019 (1983) 28-55.
Y.N. Moschovakis, Descriptive set theory. North Holland, Amsterdam (1980).
H. Rogers Jr., Theory of recursive functions and effective computability. McGraw-Hill, New York (1967).
Selivanov, V.L., Hierarchies of hyperarithmetical sets and functions. Algebra i Logika 22 (1983) 666-692 (English translation: Algebra and Logic 22 (1983) 473-491). CrossRef
V.L. Selivanov, Hierarchies, Numerations, Index Sets. Handwritten Notes (1992) 300 pp.
V.L. Selivanov, Fine hierarchy of regular ω -languages, Preprint No. 14. The University of Heidelberg, Chair of Mathematical Logic (1994) 13 pp.
V.L. Selivanov, Fine hierarchy of regular ω -languages. Springer, Berlin, Lecture Notes in Comput. Sci. 915 (1995) 277-287.
Selivanov, V.L., Fine hierarchies and Boolean terms. J. Symb. Logic 60 (1995) 289-317. CrossRef
Selivanov, V.L., Fine hierarchy of regular ω-languages. Theoret. Comput. Sci. 191 (1998) 37-59. CrossRef
V.L. Selivanov, Wadge Degrees of ω -Languages of Deterministic Turing Machines. Springer, Berlin, Lecture Notes in Comput. Sci. 2607 (2003) 97-108.
L. Staiger, ω -languages. Springer, Berlin, Handb. Formal Languages 3 (1997) 339-387.
Steel, J., Determinateness and the separation property. J. Symb. Logic 45 (1980) 143-146.
W. Wadge, Degrees of complexity of subsets of the Baire space. Notices Amer. Math. Soc. (1972) R-714.
W. Wadge, Reducibility and determinateness in the Baire space, Ph.D. Thesis. University of California, Berkeley (1984).
Wagner, K., On ω-regular sets. Inform. and Control 43 (1979) 123-177. CrossRef
R. Van Wesep, Wadge degrees and descriptive set theory. Springer, Lecture Notes in Math. 689 (1978) 151-170.