Efficient Oblivious Branching Programs for Threshold and Mod Functions

Rakesh K. Sinha, Jayram S. Thathachar

Abstract: In 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[n log3 n/log log n log log log n] 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(n log4  n) for computing general mod functions. All previously known constructions for computing general mod functions have sizeΩ(n3/2).