Recursion Schemata for NCk

Authors:
Guillaume Bonfante;Reinhard Kahle;Jean-Yves Marion;Isabel Oitavem
Affiliations:
Loria - INPL, Villers-lès-Nancy, France 54602;CENTRIA and DM, Universidade Nova de Lisboa, Caparica, Portugal 2829-516;Loria - INPL, Villers-lès-Nancy, France 54602;UNL and CMAF, Universidade de Lisboa, Lisboa, Portugal 1649-003
Venue:
CSL '08 Proceedings of the 22nd international workshop on Computer Science Logic
Year:
2008

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Abstract

We give a recursion-theoretic characterization of the complexity classes NCkfor k茂戮驴 1. In the spirit of implicit computational complexity, it uses no explicit bounds in the recursion and also no separation of variables is needed. It is based on three recursion schemes, one corresponds to time (time iteration), one to space allocation (explicit structural recursion) and one to internal computations (mutual in place recursion). This is, to our knowledge, the first exact characterization of NCkby function algebra over infinite domains in implicit complexity.