Axiomatizing resource bounds for measure

Authors:
Xiaoyang Gu;Jack H. Lutz;Satyadev Nandakumar;James S. Royer
Affiliations:
LinkedIn Corporation, Mountain View, CA;Department of Computer Science, Iowa State University, Ames, IA;Department of Computer Science and Engineering, Indian Institute of Technology Kanpur, Kanpur, UP, India;Department of Electrical Engineering and Computer Science, Syracuse University, Syracuse, NY
Venue:
CiE'11 Proceedings of the 7th conference on Models of computation in context: computability in Europe
Year:
2011

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Abstract

Resource-bounded measure is a generalization of classical Lebesgue measure that is useful in computational complexity. The central parameter of resource-bounded measure is the resource bound Δ, which is a class of functions. Most applications of resource-bounded measure use only the "measure-zero/measure-one fragment" of the theory. For this fragment, Δ can be taken to be a class of type-one functions. However, in the full theory of resource-bounded measurability and measure, the resource bound Δ also contains type-two functionals. To date, both the full theory and its zero-one fragment have been developed in terms of a list of example resource bounds. This paper replaces this list-of-examples approach with a careful investigation of the conditions that suffice for a class Δ to be a resource bound.