Implicit Complexity over an Arbitrary Structure: Quantifier Alternations

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 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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Olivier Bournez, Felipe Cucker, Paulin Jacobé de Naurois, Jean-Yves Marion. Implicit Complexity over an Arbitrary Structure: Quantifier Alternations. [Intern report] A04-R-300 || bournez04e, 2004, 23 p. ⟨inria-00107811⟩

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