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Annual Symposium on Theoretical Aspects of Computer Science

STACS 2001: STACS 2001 pp 563–574Cite as

New Bounds on the OBDD-Size of Integer Multiplication via Universal Hashing

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2010))

Abstract

Ordered binary decision diagrams (OBDDs) nowadays be- long to the most common representation types for Boolean functions. Although they allow important operations such as satisfiability test and equality test to be performed efficiently, their limitation lies in the fact that they may require exponential size for important functions. Bryant [8] has shown that any OBDD-representation of the function MULn-1;n, which computes the middle bit of the product of two n-bit numbers, requires at least 2n/8 nodes. In this paper a stronger bound of 2n/2/61 is proven by a new technique, using a recently found universal family of hash functions [23]. As a result, one cannot hope anymore to find reason- able small OBDDs even for the multiplication of relatively short integers, since for only a 64-bit multiplication millions of nodes are required. Fur- ther, a first non-trivial upper bound of 7/3. 24n/3 for the OBDD size of MULn-1;n is provided.

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Author information

Authors and Affiliations

  1. FB Informatik, LS2, Univ. Dortmund, 44221, Dortmund, Germany

    Philipp Woelfel

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  1. Philipp Woelfel
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Editors and Affiliations

  1. I3S & INRIA Sophia Antipolis INRIA, CNRS, 2004 Route des Lucioles, 06902, Sophia-Antipolis, France

    Afonso Ferreira

  2. Institut für Theoretische Informatik, Fakultät Informatik, TU Dresden, 01062, Dresden, Germany

    Horst Reichel

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© 2001 Springer-Verlag Berlin Heidelberg

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Woelfel, P. (2001). New Bounds on the OBDD-Size of Integer Multiplication via Universal Hashing. In: Ferreira, A., Reichel, H. (eds) STACS 2001. STACS 2001. Lecture Notes in Computer Science, vol 2010. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44693-1_49

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  • DOI: https://doi.org/10.1007/3-540-44693-1_49

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-41695-1

  • Online ISBN: 978-3-540-44693-4

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