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Effective category and measure in abstract complexity theory

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Fundamentals of Computation Theory (FCT 1995)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 965))

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Abstract

Strong variants of the Operator Speed-up Theorem, Operator Gap Theorem and Compression Theorem are obtained using an effective version of Baire Category Theorem. It is also shown that all complexity classes of recursive predicates have effective measure zero in the space of recursive predicates and, on the other hand, the class of predicates with almost everywhere complexity above an arbitrary recursive threshold has recursive measure one in the class of recursive predicates.

The work of the first author has been supported by Auckland University Research Grants A18/XXXXX/62090/3414012, A18/XXXXX/62090/F3414022. The second author has been partially supported by grants NSF-CCR-8957604, NSF-INT-9116781/JSPS-ENG-207 and NSF-CCR-9322513 and by the Romanian Department of Education and Science grant 4975-92.

A full version of this paper will appear in Theoret. Comput. Sc. (1996).

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Author information

Authors and Affiliations

  1. Computer Science Department, The University of Auckland, Private Bag 92109, Auckland, New Zealand

    Cristian Calude

  2. Department of Computer Science, University of Rochester, 14627, New York, USA

    Marius Zimand

Authors
  1. Cristian Calude
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  2. Marius Zimand
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Horst Reichel

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© 1995 Springer-Verlag Berlin Heidelberg

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Calude, C., Zimand, M. (1995). Effective category and measure in abstract complexity theory. In: Reichel, H. (eds) Fundamentals of Computation Theory. FCT 1995. Lecture Notes in Computer Science, vol 965. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60249-6_48

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  • DOI: https://doi.org/10.1007/3-540-60249-6_48

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