Towards an implicit characterization of NCk

Authors:
G. Bonfante;R. Kahle;J. -Y. Marion;I. Oitavem
Affiliations:
Loria, INPL, Villers-lès-Nancy, France;Dept. Matemática, Universidade de Coimbra, Apartado 3008, 3001-454 Coimbra, Portugal, and CENTRIA, UNL, Caparica, Portugal;Loria, INPL, Villers-lès-Nancy, France;CMAF, Universidade de Lisboa, Lisboa, Portugal
Venue:
CSL'06 Proceedings of the 20th international conference on Computer Science Logic
Year:
2006

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Abstract

We define a hierarchy of term systems Tk by means of restrictions of the recursion schema. We essentially use a pointer technique together with tiering. We prove Tk⊆NCk⊆Tk+1, for k ≥2. Special attention is put on the description of T2 and T3 and on the proof of T2⊆NC2⊆T3. Such a hierarchy yields a characterization of NC.