Time-space tradeoffs for branching programs contrasted with those for straight-line programs

This paper establishes time-space tradeoffs for some algebraic problems in the branching program model. For a finite field F, convolution of n-vectors over F requires ST = Θ(n2 log |F|), where S is space and T is time, in good agreement with corresponding results for straightline programs. Our result for n × n matrix multiplication over F, ST2 = Θ(n6 log |F|), is stronger than the previously known bound ST = Ω(n3) for straight-line and branching programs. The problem of computing PAQ, where P and Q are n × n permutation matrices and A is a particular matrix, requires Ω(n3) ≤ ST ≤ O(n3logn) for branching programs, in contrast to ST = Ω(n4) for straight-line programs.