Storing a Sparse Table with 0(1) Worst Case Access Time
Journal of the ACM (JACM)
Graph-Based Algorithms for Boolean Function Manipulation
IEEE Transactions on Computers
The computational complexity of universal hashing
Theoretical Computer Science - Special issue on structure in complexity theory
Communication-Space Tradeoffs for UnrestrictedProtocols
SIAM Journal on Computing
Dynamic Perfect Hashing: Upper and Lower Bounds
SIAM Journal on Computing
On the size of binary decision diagrams representing Boolean functions
Theoretical Computer Science
Improving the Variable Ordering of OBDDs Is NP-Complete
IEEE Transactions on Computers
A reliable randomized algorithm for the closest-pair problem
Journal of Algorithms
Branching programs and binary decision diagrams: theory and applications
Branching programs and binary decision diagrams: theory and applications
Efficient Strongly Universal and Optimally Universal Hashing
MFCS '99 Proceedings of the 24th International Symposium on Mathematical Foundations of Computer Science
Asymptotically Optimal Bounds for OBDDs and the Solution of Some Basic OBDD Problems
ICALP '00 Proceedings of the 27th International Colloquium on Automata, Languages and Programming
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
On the Existence of Polynomial Time Approximation Schemes for OBDD Minimization (Extended Abstract)
STACS '98 Proceedings of the 15th Annual Symposium on Theoretical Aspects of Computer Science
Bucket Hashing and its Application to Fast Message Authentication
CRYPTO '95 Proceedings of the 15th Annual International Cryptology Conference on Advances in Cryptology
A complexity theoretic approach to randomness
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
IEEE Transactions on Computers
New classes and applications of hash functions
SFCS '79 Proceedings of the 20th Annual Symposium on Foundations of Computer Science
SFCS '89 Proceedings of the 30th Annual Symposium on Foundations of Computer Science
MFCS '02 Proceedings of the 27th International Symposium on Mathematical Foundations of Computer Science
Bounds on the OBDD-size of integer multiplication via universal hashing
Journal of Computer and System Sciences
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
Exponential lower bounds on the space complexity of OBDD-Based graph algorithms
LATIN'06 Proceedings of the 7th Latin American conference on Theoretical Informatics
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Ordered binary decision diagrams (OBDDs) nowadays belong to the most common representation types for Boolean functions. Although they allow important operations such as satisfiability test and equality test to be performed efficiently, their limitation lies in the fact that they may require exponential size for important functions. Bryant [8] has shown that any OBDD-representation of the function MULn-1,n, which computes the middle bit of the product of two n-bit numbers, requires at least 2n/8 nodes. In this paper a stronger bound of 2n/2/61 is proven by a new technique, using a recently found universal family of hash functions [23]. As a result, one cannot hope anymore to find reasonable small OBDDs even for the multiplication of relatively short integers, since for only a 64-bit multiplication millions of nodes are required. Further, a first non-trivial upper bound of 7/3 ċ 24n/3 for the OBDD size of MULn-1,n is provided.