Lower bounds for depth-restricted branching programs (original) (raw)

We present a new method for proving lower bounds on the complexity of branching programs and consider k-times-only branching programs. While exponential and nearly exponential lower bounds on the complexity of one-timeonly branching programs were proved for many problems, there are still missing methods of proving lower bounds for k-times-only programs (k > 1). We prove exponential lower bounds for k-times-only branching programs which have the additional restriction that the input bits are read k times, yet blockwise and in each block in the same order. This is done both for the algebraic decision problem POLYzd (n E N prime, d<n) whether a given mapping g: IF, + F, is a polynomial over F, of degree at most d, and for the corresponding monotone problem over quadratic Boolean matrices. As a consequence we obtain a sharp bound of order @(n 'log(n)) on the communication complexity of POLY:,, (SE (0, i)).