Recursion-theoretic ranking and compression

Recursion-Theoretic Ranking and Compression

For which sets A does there exist a mapping, computed by a total or partial recursive function, such that the mapping, when its domain is restricted to A, is a 1-to-1, onto mapping to Σ * ? And for which sets A does there exist such a mapping that respects the lexicographical ordering within A? Both cases are types of perfect, minimal hash functions. The complexity-theoretic versions of these n...

A Recursion-theoretic Characterization of Constructible Reals

Let Ly denote Godel's constructive universe up to level y. A countable ordinal y is said to be an index if Ly+1 contains a real not in L r The notion was introduced by Boolos and Putnam [1] who also initiated the study (from the recursion-theoretic viewpoint) of what is known today as " the fine structure of L". In the set-theoretic context, Jensen [3] later extended their results to all levels...

Recursion Theoretic Operators for Function Complexity Classes

We characterize the gap between time and space complexity of functions by operators and completeness. First, we introduce a new notion of operators for function complexity classes based on recursive function theory and construct an operator which generates FPSPACE from FP . Then, we introduce new function classes composed of functions whose output lengths are bounded by the input length plus so...

Learning to Coordinate; a Recursion Theoretic Perspective

We consider two players each of whom attempts to predict the behavior of the other, using no more than the history of earlier predictions. Behaviors are limited to a pair of options, conventionally denoted by 0, 1. Such players face the problem of learning to coordinate choices. The present paper formulates their situation recursion theoretically, and investigates the prospects for success. A p...

A Recursion-theoretic View of Axiomatizable Theories