Two functions algebras defining functions in NC^k boolean circuits

Guillaume Bonfante, Reinhard Kahle, Jean-Yves Marion, Isabel Oitavem

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)


We describe the functions computed by boolean circuits in NCk by means of functions algebra for k >= 1 in the spirit of implicit computational complexity. The whole hierarchy defines NC. In other words, we give a recursion-theoretic characterization of the complexity classes NCk for k >= 1 without reference to a machine model, nor explicit bounds in the recursion schema. Actually, we give two equivalent descriptions of the classes NCk, k >= 1. One is based on a tree structure a la Leivant, the other is based on words. This latter puts into light the role of computation of pointers in circuit complexity. We show that transducers are a key concept for pointer evaluation.
Original languageEnglish
Pages (from-to)82-103
Number of pages22
JournalInformation and Computation
Publication statusPublished - Jun 2016


  • Boolean circuits
  • NCk
  • Parallel computation class
  • Transducers


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