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
Symbolic OBDD-Based Reachability Analysis Needs Exponential Space
SOFSEM '10 Proceedings of the 36th Conference on Current Trends in Theory and Practice of Computer Science
Larger lower bounds on the OBDD complexity of integer multiplication
Information and Computation
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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Integer multiplication as one of the basic arithmetic functionshas been in the focus of several complexity theoreticalinvestigations and ordered binary decision diagrams (OBDDs) are oneof the most common dynamic data structures for Boolean functions.Analyzing the limits of symbolic graph algorithms for thereachability problem Sawitzki (2006) has presented the firstexponential lower bound on the π-OBDD size for the mostsignificant bit of integer multiplication according to onepredefined variable order π. Since the choice of thevariable order is a main issue to obtain OBDDs of small size theinvestigation is continued. As a result a new upper bound methodand the first non-trivial upper bound on the size of OBDDsaccording to an arbitrary variable order is presented. Furthermore,Sawitzki's lower bound is improved.