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Two function algebras defining functions in NC k boolean circuits

Abstract : We describe the functions computed by boolean circuits in NCk by means of func- tions algebra for k ≥ 1 in the spirit of implicit computational complexity. The whole hierarchy defines NC. In other words, we give a recursion-theoretic charac- terization 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 equiv- alent description of the classes NCk, f ≥ 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.
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Submitted on : Thursday, February 5, 2015 - 1:15:32 PM
Last modification on : Friday, July 8, 2022 - 10:05:14 AM
Long-term archiving on: : Wednesday, May 6, 2015 - 10:15:25 AM


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Guillaume Bonfante, Reinhard Kahle, Jean-Yves Marion, Isabel Oitavem. Two function algebras defining functions in NC k boolean circuits. Information and Computation, Elsevier, 2016, ⟨10.1016/j.ic.2015.12.009⟩. ⟨hal-01113342⟩



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