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On tiered small jump operators

Identifieur interne : 003D74 ( Main/Merge ); précédent : 003D73; suivant : 003D75

On tiered small jump operators

Source :

Logical Methods in Computer Science [ 1860-5974 ] ; 2009.

RBID : Hal:hal-00439624

Abstract

Predicative analysis of recursion schema is a method to characterize complexity classes like the class FPTIME of polynomial time computable functions. This analysis comes from the works of Bellantoni and Cook, and Leivant by data tiering. Here, we refine predicative analysis by using a ramified Ackermann's construction of a non-primitive recursive function. We obtain a hierarchy of functions which characterizes exactly functions, which are computed in O(n^k) time over register machine model of computation. For this, we introduce a strict ramification principle. Then, we show how to diagonalize in order to obtain an exponential function and to jump outside deterministic polynomial time. Lastly, we suggest a dependent typed lambda-calculus to represent this construction.

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https://hal.archives-ouvertes.fr/hal-00439624

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Le document en format XML

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On tiered small jump operators

On tiered small jump operators

Source :

Abstract

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Links to Exploration step

Le document en format XML

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