A recursion-theoretic approach to NP

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 Progressive Approach to Recursion

We propose a progressive approach to simplify teaching recursion. It is introduced by means of three instances of increasing level of difficulty. First, recursion is introduced in a “pure” form as it is found in formal grammars; its accompanying mechanisms are related to rewriting. Later, a functional programming language allows defining recursive functions and recursive data types; its mechani...

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...

A Recursion-theoretic View of Axiomatizable Theories

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...