WC give a characterization of span program size by a combinatorial-algebraic measure defined on covers of pairs of O’s and l’s of the function computed. The measure we consider is a generalization of… (More)

In this paper we obtain the first superpolynomial lower bounds for monotone span programs computing explicit functions. The best previous lower bound was Ω(n) by Beimel, Gál, Paterson [BGP]; our… (More)

In the multiparty communication game (CFL-game) of Chandra, Furst, and Lipton (Proc. 15th ACM STOC, 1983, 94–99) k players collaboratively evaluate a function f(x0, . . . , xk−1) in which player i… (More)

This paper contains two main results. The first is an explicit construction of bipartite graphs which do not contain certain complete bipartite subgraphs and have maximal density, up to a constant… (More)

We consider the question: Is nding just a part of a solution easier than nding the full solution? For example, is nding only an fraction of the bits in a satisfying assignment to a 3-CNF formula… (More)

This paper provides logspace and small circuit depth analogs of the result of Valiant and Vazirani, which is a randomized (or nonuniform) reduction from $NP$ to its arithmetic analog $\plusminus P$.… (More)

We shall give simpler proofs of some lower bounds on monotone computations. We describe a simple cond combinatorial structures, such that the rank of the matrix associated with these structures gives… (More)