An Upper Bound for a Communication Game Related to Time-Space Tradeoffs

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 Erdos, Frankl and Rodl [5] of a large 3-hypergraph with no 3 distinct edges whose union has at most 6 vertices. 1 Introduction Suppose that we have two vectors u and v of length k. We want to decide whether u = v, but our access to the bits is very limited---at any moment we can see at most one bit of each pair of the bits u i and v i . You can imagine the corresponding bits to be written on two sides of a card, so that we can see all the cards but only one side of each card. After every flip we can write down some information, but the memory is not reusable---after the next flip we have to use new memory. We are charged for every bit of memory that we use and for every time we flip one or more cards. It seems natural to sup..

An Upper Bound for a Communication Game Related to Time-Space Tradeoffs

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 Erdös, Frankl and Rödl [5] of a large 3-hypergraph with no 3 distinct edges whose union has at most 6 vertices