Computation Times of Arithmetic and Boolean Functions in (d, r) Circuits

A (d, r) circuit is a d-valued logical circuit in which each element has fan-in at most r and can compute any r-argument d-valued logical function in unit time. In this paper we review results previously published on the computation time of such circuits for addition and multiplication and for computation of general Boolean functions. We also explicitly state hitherto unpublished but known results on the time necessary to divide in such circuits.