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Lower Bounds on the OBDD Size of Graphs of Some Popular Functions

  • Conference paper
SOFSEM 2005: Theory and Practice of Computer Science (SOFSEM 2005)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3381))

Abstract

Ordered 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.

An extended version of this paper is available via http://ls2-www.cs.uni-dortmund.de/ sawitzki/LBotOSoGoSPF_Extended.pdf.

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Author information

Authors and Affiliations

  1. University of Dortmund, Computer Science 2, D-44221, Dortmund, Germany

    Daniel Sawitzki

Authors
  1. Daniel Sawitzki
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Editor information

Editors and Affiliations

  1. Charles University, Prague, Czech Republic

    Peter Vojtáš

  2. Institute of Informatics and Software Engineering Faculty of Informatics and Information technologies, Slovak University of Technology, Ilkovičova 3, 842 16, Bratislava,  

    Mária Bieliková

  3. STIX, École Polytechnique, 91128, Palaiseau Cedex, France

    Bernadette Charron-Bost

  4. Department of Computer Science, University of Loughborough, Loughborough, UK

    Ondrej Sýkora

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Sawitzki, D. (2005). Lower Bounds on the OBDD Size of Graphs of Some Popular Functions. In: Vojtáš, P., Bieliková, M., Charron-Bost, B., Sýkora, O. (eds) SOFSEM 2005: Theory and Practice of Computer Science. SOFSEM 2005. Lecture Notes in Computer Science, vol 3381. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30577-4_33

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  • DOI: https://doi.org/10.1007/978-3-540-30577-4_33

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-24302-1

  • Online ISBN: 978-3-540-30577-4

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