Graph-Based Algorithms for Boolean Function Manipulation
IEEE Transactions on Computers
Symbolic Boolean manipulation with ordered binary-decision diagrams
ACM Computing Surveys (CSUR)
The graph of multiplication is equivalent to counting
Information Processing Letters
Information Processing Letters
Efficient data structures for Boolean functions
Discrete Mathematics - Special issue: trends in discrete mathematics
On lower bounds for read-k-times branching programs
Computational Complexity
A lower bound for integer multiplication with read-once branching programs
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
Communication complexity and parallel computing
Communication complexity and parallel computing
Communication complexity
Branching programs and binary decision diagrams: theory and applications
Branching programs and binary decision diagrams: theory and applications
Lower Bounds for One-way Probabilistic Communication Complexity
ICALP '93 Proceedings of the 20th International Colloquium on Automata, Languages and Programming
On the Power of Randomized Branching Programs
ICALP '96 Proceedings of the 23rd International Colloquium on Automata, Languages and Programming
Randomization and Nondeterminism Are Comparable for Ordered Read-Once Branching Programs
ICALP '97 Proceedings of the 24th International Colloquium on Automata, Languages and Programming
Lower Bounds for Deterministic and Nondeterministic Branching Programs
FCT '91 Proceedings of the 8th International Symposium on Fundamentals of Computation Theory
Some complexity questions related to distributive computing(Preliminary Report)
STOC '79 Proceedings of the eleventh annual ACM symposium on Theory of computing
Restricted Branching Programs and Hardware Verification
Restricted Branching Programs and Hardware Verification
On the computational power of probabilistic and quantum branching program
Information and Computation
Better upper bounds on the QOBDD size of integer multiplication
Discrete Applied Mathematics
On the computational power of probabilistic and quantum branching program
Information and Computation
Randomized OBDDs for the most significant bit of multiplication need exponential space
Information Processing Letters
Randomized OBDDs for the most significant bit of multiplication need exponential size
SOFSEM'11 Proceedings of the 37th international conference on Current trends in theory and practice of 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
The complexity of classical and quantum branching programs: a communication complexity approach
SAGA'05 Proceedings of the Third international conference on StochasticAlgorithms: foundations and applications
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We prove an exponential lower bound 2Ω(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 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.