Sam Buss ; Douglas Cenzer ; Jeffrey B. Remmel - Sub-computable Boundedness Randomness

lmcs:979 - Logical Methods in Computer Science, December 24, 2014, Volume 10, Issue 4 - https://doi.org/10.2168/LMCS-10(4:15)2014
Sub-computable Boundedness RandomnessArticle

Authors: Sam Buss ORCID; Douglas Cenzer ; Jeffrey B. Remmel

    This paper defines a new notion of bounded computable randomness for certain classes of sub-computable functions which lack a universal machine. In particular, we define such versions of randomness for primitive recursive functions and for PSPACE functions. These new notions are robust in that there are equivalent formulations in terms of (1) Martin-Löf tests, (2) Kolmogorov complexity, and (3) martingales. We show these notions can be equivalently defined with prefix-free Kolmogorov complexity. We prove that one direction of van Lambalgen's theorem holds for relative computability, but the other direction fails. We discuss statistical properties of these notions of randomness.

    https://doi.org/10.2168/LMCS-10(4:15)2014
    Source: arXiv.org:1411.3995
    Volume: Volume 10, Issue 4
    Published on: December 24, 2014
    Imported on: January 27, 2014
    Keywords: Computer Science - Logic in Computer Science
    Licence: arXiv.org - Non-exclusive license to distribute
    Funding:
      Source : OpenAIRE Graph
    • Complexity of proofs, proof search, and algorithmic complexity; Funder: National Science Foundation; Code: 1101228
    • AF: Large: Collaborative Research: Exploiting Duality between Meta-Algorithms and Complexity; Funder: National Science Foundation; Code: 1213151

    Classifications

    Mathematics Subject Classification 20201
    Sources:
    • [1] zbMATH Open.

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