Abstract
We give a recursion-theoretic characterization of the complexity classes NCk for k ≥ 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 NCk by function algebra over infinite domains in implicit complexity.
Research supported by the project Teorias e linguagens de programação para computações com recursos limitados within the Programa PESSOA 2005/2006 of GRICES - EGIDE and partly by the FCT project POCI/MAT/61720/2004 and by DM, FCT-UNL.This work was complete while the first author visited CMAF, Universidade de Lisboa, and the support of the visit is gratefully acknowledged.
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Bonfante, G., Kahle, R., Marion, JY., Oitavem, I. (2008). Recursion Schemata for NCk . In: Kaminski, M., Martini, S. (eds) Computer Science Logic. CSL 2008. Lecture Notes in Computer Science, vol 5213. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-87531-4_6
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DOI: https://doi.org/10.1007/978-3-540-87531-4_6
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