Recursion Schemata for NCk

  • Guillaume Bonfante
  • Reinhard Kahle
  • Jean-Yves Marion
  • Isabel Oitavem
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5213)


We give a recursion-theoretic characterization of the complexity classes NC k 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 NC k by function algebra over infinite domains in implicit complexity.


Boolean Function Binary Tree Turing Machine Auxiliary Function Computation Tree 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Guillaume Bonfante
    • 1
  • Reinhard Kahle
    • 2
  • Jean-Yves Marion
    • 1
  • Isabel Oitavem
    • 3
  1. 1.Loria - INPLVillers-lès-NancyFrance
  2. 2.CENTRIA and DMUniversidade Nova de LisboaCaparicaPortugal
  3. 3.UNL and CMAFUniversidade de LisboaLisboaPortugal

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