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Sub-computable Bounded Pseudorandomness

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Logical Foundations of Computer Science (LFCS 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7734))

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Abstract

This paper defines a new notion of bounded pseudorandomness for certain classes of sub-computable functions where one does not have access to a universal machine for that class within the class. In particular, we define such a version of randomness for the class of primitive recursive functions and a certain subclass of PSPACE functions. Our new notion of primitive recursive bounded pseudorandomness is robust in that there are equivalent formulations in terms of (1) Martin-Löf tests, (2) Kolmogorov complexity, and (3) martingales.

Cenzer was partially supported by the NSF grant DMS-652372.

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Florida, P.O. Box 118105, Gainesville, Florida, 32611, USA

    Douglas Cenzer

  2. Department of Mathematics, University of California, San Diego, La Jolla, CA, 92093-0112, USA

    Jeffrey B. Remmel

Authors
  1. Douglas Cenzer
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  2. Jeffrey B. Remmel
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Editor information

Editors and Affiliations

  1. Computer Science, CUNY Graduate Center, 365 Fifth Avenue, 10016, New York, NY, USA

    Sergei Artemov

  2. Department of Mathematics, Cornell University, 545 Malott Hall, 14853, Ithaca, NY, USA

    Anil Nerode

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Cenzer, D., Remmel, J.B. (2013). Sub-computable Bounded Pseudorandomness. In: Artemov, S., Nerode, A. (eds) Logical Foundations of Computer Science. LFCS 2013. Lecture Notes in Computer Science, vol 7734. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35722-0_8

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  • DOI: https://doi.org/10.1007/978-3-642-35722-0_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-35721-3

  • Online ISBN: 978-3-642-35722-0

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