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Journal Articles Information and Computation Year : 2006

Implicit Complexity over an Arbitrary Structure: Quantifier Alternations

Abstract

We provide machine-independent characterizations of some complexity classes, over an arbitrary structure, in the model of computation proposed by L. Blum, M. Shub and S. Smale. We show that the levels of the polynomial hierarchy correspond to safe recursion with predicative minimization and the levels of the digital polynomial hierarchy to safe recursion with digital predicative minimization. Also, we show that polynomial alternating time corresponds to safe recursion with predicative substitutions and that digital polynomial alternating time corresponds to safe recursion with digital predicative substitutions.
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Dates and versions

inria-00000516 , version 1 (26-10-2005)

Identifiers

  • HAL Id : inria-00000516 , version 1

Cite

Olivier Bournez, Felipe Cucker, Paulin Jacobé de Naurois, Jean-Yves Marion. Implicit Complexity over an Arbitrary Structure: Quantifier Alternations. Information and Computation, 2006, 204 (2), pp.210--230. ⟨inria-00000516⟩
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