An upper bound for a communication game related to time-space tradeoffs

Abstract

We prove an unexpected upper bound on a communication game proposed by Jeff Edmonds and Russell Impagliazzo [2, 3] as an approach for proving lower bounds for time-space tradeoffs for branching programs. Our result is based on a generalization of a construction of Erdős, Frankl and Rödl [5] of a large 3-hypergraph with no 3 distinct edges whose union has at most 6 vertices.