Two function algebras defining functions in NC k boolean circuits - Bonfante, Guillaume; Kahle, Reinhard; Marion, Jean-Yves; Oitavem, Isabel (Information and computation, 2016)
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.