Two function algebras defining functions in NC k boolean circuits

Guillaume Bonfante (1) , Reinhard Kahle (2) , Jean-Yves Marion (1) , Isabel Oitavem (2)

1 CARTE - Theoretical adverse computations, and safety
2 DI - Departamento de Informática

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.

Mots clés: NCk; Boolean circuits; transducers; parallel computation class

Domaines: Informatique [cs]; Complexité [cs.CC]

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