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On maximal QROBDD's of Boolean functions

Published online by Cambridge University Press:  15 October 2005

Jean-Francis Michon
Affiliation:
Université de Rouen, LIFAR, 75821 Mont Saint Aignan Cedex, France; jean.francis.michon@univ-rouen.fr; pierre.valarcher@univ-rouen.fr
Jean-Baptiste Yunès
Affiliation:
Université Paris 7, LIAFA, 175 rue du Chevaleret, 75013 Paris, France; Jean-Baptiste.Yunes@liafa.jussieu.fr
Pierre Valarcher
Affiliation:
Université de Rouen, LIFAR, 75821 Mont Saint Aignan Cedex, France; jean.francis.michon@univ-rouen.fr; pierre.valarcher@univ-rouen.fr
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Abstract

We investigate the structure of “worst-case” quasi reduced ordered decision diagrams and Boolean functions whose truth tables are associated to: we suggest different ways to count and enumerate them. We, then, introduce a notion of complexity which leads to the concept of “hard” Boolean functions as functions whose QROBDD are “worst-case” ones. So we exhibit the relation between hard functions and the Storage Access function (also known as Multiplexer).

Type
Research Article
Copyright
© EDP Sciences, 2005

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References

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Heap, M. and Mercer, M.R., Least upper bounds on obdd sizes. IEEE Trans. Comput. 43 (1994) 764767. CrossRef
J.F. Michon, P. Valarcher and J.B. Yunès, Integer sequence number a100344. stored in The On-Line Encyclopedia of Integer Sequence, N.J.A. Sloane, published electronically at http://www.research.att.com/~njas/sequences (2004).
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