Abstract
AbstractOrdered binary decision diagrams (OBDDs) are a data structure for Boolean functions which supports many useful operations. It finds many applications in logic design, CAD, model checking, and symbolic graph algorithms. Nevertheless, many simple functions are known to have exponential OBDD size w. r. t. their number of variables. In order to investigate the limits of symbolic graph algorithms which work on OBDD-represented graph instances, it is useful to have simply-structured graphs whose OBDD representation has exponential size. Therefore, we consider fundamental arithmetic and storage access functions with exponential OBDD size and transfer these results to the graphs of these functions. Concretely, lower bounds for the graphs of integer multiplication, indirect storage access, and the hidden weighted bit function are presented. Finally, an exemplary application of the result for multiplication to the analysis of a symbolic all-pairs shortest-paths algorithm is sketched.KeywordsModel CheckBoolean FunctionArithmetic FunctionBinary Decision DiagramLogic DesignThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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