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
On the size of binary decision diagrams representing Boolean functions
Theoretical Computer Science
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
Improving the Variable Ordering of OBDDs Is NP-Complete
IEEE Transactions on Computers
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
New Bounds on the OBDD-Size of Integer Multiplication via Universal Hashing
STACS '01 Proceedings of the 18th Annual Symposium on Theoretical Aspects 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
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
A larger lower bound on the OBDD complexity of the most significant bit of multiplication
LATIN'10 Proceedings of the 9th Latin American conference on Theoretical Informatics
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Bryant [On the complexity of VLSI implementations and graph representations of boolean functions with applications to integer multiplication, IEEE Trans. Comput. 40 (1991) 205-213] has shown that any OBDD for the function MUL"n"-"1","n, i.e. the middle bit of the n-bit multiplication, requires at least 2^n^/^8 nodes. In this paper a stronger lower bound of essentially 2^n^/^2/61 is proven by a new technique, using a universal family of hash functions. As a consequence, one cannot hope anymore to verify e.g. 128-bit multiplication circuits using OBDD-techniques because the representation of the middle bit of such a multiplier requires more than 3.10^1^7OBDD-nodes. Further, a first non-trivial upper bound of 7/3.2^4^n^/^3 for the OBDD-size of MUL"n"-"1","n is provided.