MFCS '02 Proceedings of the 27th International Symposium on Mathematical Foundations of Computer Science
Time-space tradeoff lower bounds for integer multiplication and graphs of arithmetic functions
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
On the OBDD complexity of the most significant bit of integer multiplication
TAMC'08 Proceedings of the 5th international conference on Theory and applications of models of computation
On the OBDD complexity of the most significant bit of integer multiplication
Theoretical Computer Science
Lower bounds on the OBDD size of graphs of some popular functions
SOFSEM'05 Proceedings of the 31st international conference on Theory and Practice of Computer Science
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Branching Programs (BPs) are a well-established computation and representation model for Boolean functions. Although exponential lower bounds for restricted BPs such as Read-Once Branching Programs (BP1s) have been known for a long time, the proof of lower bounds for important selected functions is sometimes difficult. Especially the complexity of fundamental functions such as integer multiplication in different BP models is interesting.Bollig and Woelfel (2001) have proven the first strongly exponential lower bound of Omega(2^(n/4)) for the complexity of integer multiplication in the deterministic BP1 model. Here, we consider two well-studied BP models which generalize BP1s by allowing a limited amount of nondeterminism and multiple variable tests, respectively. More precisely, we prove a lower bound of Omega(2^(n/(7k))) for the complexity of integer multiplication in the (OR,k)-BP model. As a corollary, we obtain that integer multiplication cannot be represented in polynomial size by nondeterministic BP1s, if the number of nondeterministic nodes is bounded by log n - loglog n - omega(1). Furthermore, we show that any (1,+k)-BP representing integer multiplication has a size of Omega[2^(n/(48(k+1)))]. This is not polynomial for k=o(n/log n).