A Lower Bound for Integer Multiplication on Randomized Ordered Read-Once Branching Programs.

Farid Ablayev, Marek Karpinski: A Lower Bound for Integer Multiplication on Randomized Ordered Read-Once Branching Programs CSIT 1999 : E/E

Abstract

We prove an exponential lower bound ($2^{\Omega(n/\log n)}$) 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 common models of randomized branching programs. In contrast, we prove that testing integer multiplication, contrary even to nondeterministic situation, can be computed by randomized ordered read-once 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.

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Printed Edition

Ch. Freytag and V. Wolfengagen (Eds.): CSIT'99, Proceedings of 1st International Workshop on Computer Science and Information Technologies, January 18-22, 1999, Moscow, Russia. MEPhI Publishing 1999, ISBN 5-7262-0263-5

Electronic Edition