On the Parallel Evaluation of Polynomials

If an unlimited number of processors is available, then for any given number of steps s, s≥1, polynomials of degree as large as C2
^n-δ
can be evaluated, where C= √2 and δ ≈ √2s. This implies polynomials of degree can be evaluated in log
2
n+√2log
2
n +0(1) steps. Various techniques for the evaluation of polynomials in a "reasonable number" of "steps" are compared with the known lower bounds.