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Article Dans Une Revue Logical Methods in Computer Science Année : 2009

On tiered small jump operators

Résumé

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.

Dates et versions

hal-00439624 , version 1 (08-12-2009)

Identifiants

Citer

Jean-Yves Marion. On tiered small jump operators. Logical Methods in Computer Science, 2009, 5 (1), pp.1-19. ⟨10.2168/LMCS-5(1:7)2009⟩. ⟨hal-00439624⟩
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