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
Secondary volumes: Selected Papers of the 10th International Conference on Computability and Complexity in Analysis (CCA 2013)
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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