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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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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