Efficient Oblivious Branching Programs for Threshold and Mod Functions

AbstractIn his survey paper on branching programs, Razborov asked the following question: Does every rectifier-switching network computing the majority ofnbits have sizen1+Ω(1)? We answer this question in the negative by constructing a simple oblivious branching program of sizeO[nlog3n/loglognlogloglogn] for computing any threshold function. This improves the previously best known upper bound ofO(n3/2) due to Lupanov. We also construct oblivious branching programs of sizeo(nlog4n) for computing general mod functions. All previously known constructions for computing general mod functions have sizeΩ(n3/2)