Graph-Based Algorithms for Boolean Function Manipulation
IEEE Transactions on Computers
Information Processing Letters
Communication complexity and parallel computing
Communication complexity and parallel computing
Communication complexity
A Lower Bound for Integer Multiplication with Read-Once Branching Programs
SIAM Journal on Computing
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
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
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
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
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
Larger lower bounds on the OBDD complexity of integer multiplication
Information and Computation
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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 the most common dynamic data structure for Boolean functions. Among the many areas of application are verification, model checking, computer-aided design, relational algebra, and symbolic graph algorithms. Analyzing the limits of symbolic graph algorithms for the all-pairs-shortest paths problem which work on OBDD-represented graph instances the so-called graph of integer multiplication has been investigated by Sawitzki [D. Sawitzki, Lower bounds on the OBDD size of graphs of some popular functions, in: Proc. of SOFSEM, LNCS, vol. 3381, 2005, pp. 298-309]. Using simple arguments his lower bound of 2^n^/^7^6^8^-^1 on the size of OBDDs representing the graph of integer multiplication is improved up to 2^n^/^2^4.