The computational complexity of universal hashing
Theoretical Computer Science - Special issue on structure in complexity theory
Information Processing Letters
On lower bounds for read-k-times branching programs
Computational Complexity
A reliable randomized algorithm for the closest-pair problem
Journal of Algorithms
Determinism versus non-determinism for linear time RAMs (extended abstract)
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
A Lower Bound for Integer Multiplication with Read-Once Branching Programs
SIAM Journal on Computing
Branching programs and binary decision diagrams: theory and applications
Branching programs and binary decision diagrams: theory and applications
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Time-space tradeoffs, multiparty communication complexity, and nearest-neighbor problems
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Time-space tradeoffs for branching programs
Journal of Computer and System Sciences
MFCS '02 Proceedings of the 27th International Symposium on Mathematical Foundations of Computer Science
Universal Hashing and k-Wise Independent Random Variables via Integer Arithmetic without Primes
STACS '96 Proceedings of the 13th Annual Symposium on Theoretical Aspects of Computer Science
TCS '02 Proceedings of the IFIP 17th World Computer Congress - TC1 Stream / 2nd IFIP International Conference on Theoretical Computer Science: Foundations of Information Technology in the Era of Networking and Mobile Computing
A Non-Linear Time Lower Bound for Boolean Branching Programs
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Super-linear time-space tradeoff lower bounds for randomized computation
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
CCC '02 Proceedings of the 17th IEEE Annual Conference on Computational Complexity
Bounds on the OBDD-size of integer multiplication via universal hashing
Journal of Computer and System Sciences
Approximating Boolean functions by OBDDs
Discrete Applied Mathematics
Better upper bounds on the QOBDD size of integer multiplication
Discrete Applied Mathematics
A note on the size of OBDDs for the graph of integer multiplication
Information Processing Letters
Larger Lower Bounds on the OBDD Complexity of Integer Multiplication
LATA '09 Proceedings of the 3rd International Conference on Language and Automata Theory and Applications
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
Randomized OBDDs for the most significant bit of multiplication need exponential space
Information Processing Letters
Larger lower bounds on the OBDD complexity of integer multiplication
Information and Computation
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
On the OBDD complexity of the most significant bit of integer multiplication
Theoretical Computer Science
Discrete Applied Mathematics
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We prove exponential size lower bounds for nondeterministic and randomized read-k BPs as well as a time-space tradeoff lower bound for unrestricted, deterministic multi-way BPs computing the middle bit of integer multiplication. The lower bound for randomized read-k BPs is superpolynomial as long as the error probability is superpolynomially small. For polynomially small error, we have a polynomial upper bound on the size of approximating read once BPs for this function. The lower bounds follow from a more general result for the graphs of universal hash classes that is applicable to the graphs of arithmetic functions such as integer multiplication, convolution, and finite field multiplication.