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RAIRO - Theoretical Informatics and Applications RAIRO - Theoretical Informatics and Applications

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On maximal QROBDD's of Boolean functions

Published online by Cambridge University Press:  15 October 2005

Jean-Francis Michon ,
Jean-Baptiste Yunès  and
Pierre Valarcher
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).

Keywords

Boolean functions Boolean complexity Boolean graphs binary decision diagrams BDD OBDD
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 39 , Issue 4 , October 2005 , pp. 677 - 686
Copyright
© EDP Sciences, 2005

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References

R.E. Bryant, Graph based algorithms for boolean function manipulation. IEEE Trans. Comput. C-35 (1986) 677–691.
C. Gröpl, Binary Decision Diagrams for Random Boolean Functions. Ph.D. Thesis, Humboldt-Universität zu Berlin (1999).
Gröpl, C., Prömel, H.J. and Srivastav, A., Size and structure of random ordered binary decision diagrams (extended abstract), in STACS'98, Springer Verlag. Lect. Notes Comput. Sci. 1373 (1998) 238–248. CrossRef
Gröpl, C., Prömel, H.J. and Srivastav, A., On the evolution of the worst-case obdd size. Inform. Process. Lett. 77 (2001) 1–7. CrossRef
Heap, M. and Mercer, M.R., Least upper bounds on obdd sizes. IEEE Trans. Comput. 43 (1994) 764–767. 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).
Paul, W., A 2.5n lower bound on the combinatorial complexity of boolean functions. SIAM J. Comput. 6 (1977) 427–443. CrossRef
I. Wegener, The complexity of Boolean functions. Wiley (1987).
I. Wegener, Branching programs and binary decision diagrams. SIAM Monogr. Discrete Math. Appl. (2000).

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