Graph-Based Algorithms for Boolean Function Manipulation
IEEE Transactions on Computers
Reduced order LQG controllers for linear time varying plants
Systems & Control Letters
Information Processing Letters
Communication complexity and parallel computing
Communication complexity and parallel computing
Communication complexity
Computing strongly connected components in a linear number of symbolic steps
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
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
Bounds on the OBDD-size of integer multiplication via universal hashing
Journal of Computer and System Sciences
Theoretical Computer Science
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
New Results on the Most Significant Bit of Integer Multiplication
ISAAC '08 Proceedings of the 19th International Symposium on Algorithms and Computation
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
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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Integer multiplication as one of the basic arithmetic functions has been in the focus of several complexity theoretical investigations and ordered binary decision diagrams (OBDDs) are one of the most common dynamic data structures for Boolean functions. Recently, the question whether the OBDD complexity of the most significant bit of integer multiplication is exponential has been answered affirmatively. In this paper a larger general lower bound is presented using a simpler proof. Furthermore, we prove a larger lower bound for the variable order assumed to be one of the best ones for the most significant bit. Moreover, the best known lower bound on the OBDD complexity for the so-called graph of integer multiplication is improved.