Computability over an Arbitrary Structure. Sequential and Parallel Polynomial Time

Olivier Bournez 1 Felipe Cucker Paulin Jacobé de Naurois 1 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 computable functions over any arbitrary structure can be characterized in term of safe recursive functions. We show that polynomial parallel time decision problems over any arbitrary structure can be characterized in terms of safe recursive functions with substitutions.
Mots-clés : complexité safe recursion complexity blum shub smale model modèle de blum shub smale récursion sûre
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Conference papers
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https://hal.inria.fr/inria-00099618
Contributor : Publications Loria <>
Submitted on : Tuesday, September 26, 2006 - 9:39:28 AM
Last modification on : Thursday, January 11, 2018 - 6:19:58 AM

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Olivier Bournez, Felipe Cucker, Paulin Jacobé de Naurois, Jean-Yves Marion. Computability over an Arbitrary Structure. Sequential and Parallel Polynomial Time. Foundations of Software Science and Computation Structures - FOSSACS'03, Apr 2003, Warsaw, Poland, pp.185-199. ⟨inria-00099618⟩

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