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 Randomness

Authors: Sam Buss ; 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.


Volume: Volume 10, Issue 4
Published on: December 24, 2014
Accepted on: June 25, 2015
Submitted on: January 27, 2014
Keywords: Computer Science - Logic in Computer Science


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