Implicit Complexity Over an Arbitrary Structure: Sequential and Parallel Polynomial Time.

Olivier Bournez 1 Felipe Cucker Paulin Jacobé de Naurois Jean-Yves Marion 2
1 PROTHEO - Constraints, automatic deduction and software properties proofs
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
2 CALLIGRAMME - Linear logic, proof networks and categorial grammars
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
Abstract : We provide several machine-independent characterizations of deterministic complexity classes in the model of computation proposed by L. Blum, M. Shub and S. Smale. We provide a characterization of partial recursive functions over any arbitrary structure. We show that polynomial time over an arbitrary structure can be characterized in terms of safe recursion. We show that polynomial parallel time over an arbitrary structure can be characterized in terms of safe recursion with substitutions.
Keywords : Blum Shub Smale model implicit complexity complexity theory
Document type :
Journal articles
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https://hal.inria.fr/inria-00102942
Contributor : Olivier Bournez <>
Submitted on : Monday, October 2, 2006 - 10:06:19 PM
Last modification on : Thursday, January 11, 2018 - 6:19:57 AM

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  • HAL Id : inria-00102942, version 1

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Olivier Bournez, Felipe Cucker, Paulin Jacobé de Naurois, Jean-Yves Marion. Implicit Complexity Over an Arbitrary Structure: Sequential and Parallel Polynomial Time.. Journal of Logic and Computation, Oxford University Press (OUP), 2005, 15 (1), pp.41--58. ⟨inria-00102942⟩

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