A lower bound for integer multiplication on randomized ordered read-once branching programs

Farid Ablayev, Marek Karpinski
2003 Information and Computation  
We prove an exponential lower bound 2 (n/ log n) on the size of any randomized ordered read-once branching program computing integer multiplication. Our proof depends on proving a new lower bound on Yao's randomized one-way communication complexity of certain Boolean functions. It generalizes to some other models of randomized branching programs. In contrast, we prove that testing integer multiplication, contrary even to a nondeterministic situation, can be computed by randomized ordered
more » ... ce branching program in polynomial size. It is also known that computing the latter problem with deterministic read-once branching programs is as hard as factoring integers.
doi:10.1016/s0890-5401(03)00118-4 fatcat:hk36x4iylzbrdd4e5dt2lfiwoi