Abstract
Ordered binary decision diagrams (OBDDs) and their variants are motivated by the need to represent Boolean functions in applications. Research concerning these applications leads also to problems and results interesting from a theoretical point of view. In this paper, methods from communication complexity and information theory are combined to prove that the direct storage access function and the inner product function have the following property. They have linear π-OBDD size for some variable ordering π and, for most variable orderings π’, all functions which approximate them on considerably more than half of the inputs, need exponential π’-OBDD size. These results have implications for the use of OBDDs in experiments with genetic programming.
Supported by DFG grant Kr 1521/3-1.
The research was partially supported by GA of the Czech Republic, Grant No. 201/98/0717.
Supported by DFG grant We 1066/8-1 and by the DFG as part of the Collaborative Research Center “Computational Intelligence” (531).
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Krause, M., Savický, P., Wegener, I. (1999). Approximations by OBDDs and the Variable Ordering Problem. In: Wiedermann, J., van Emde Boas, P., Nielsen, M. (eds) Automata, Languages and Programming. Lecture Notes in Computer Science, vol 1644. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48523-6_46
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