Computability over an arbitrary structure: sequential and parallel polynomial time

  • Authors:
  • Olivier Bournez;Felipe Cucker;Paulin Jacobé de Naurois;Jean-Yves Marion

  • Affiliations:
  • LORIA, Villers-lès-Nancy Cedex, Nancy, France;City University of Hong Kong, Kowloon, Hong Kong;LORIA, Villers-lès-Nancy Cedex, Nancy, France;LORIA, Villers-lès-Nancy Cedex, Nancy, France

  • Venue:
  • FOSSACS'03/ETAPS'03 Proceedings of the 6th International conference on Foundations of Software Science and Computation Structures and joint European conference on Theory and practice of software
  • Year:
  • 2003

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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.