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Symposium on Recursive Combinatorics

LaM 1983: Logic and Machines: Decision Problems and Complexity pp 397–407Cite as

The VLSI complexity of Boolean functions

  • Section VI: Complexity Of Boolean Functions
  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 171))

Abstract

It is well-known that all Boolean functions of n variables can be computed by a logic circuit with O(2n/n) gates (Lupanov's theorem) and that there exist Boolean functions of n variables which require logic circuits of this size (Shannon's theorem). We present corresponding results for Boolean functions computed by VLSI circuits, using Thompson's model of a VLSI chip. We prove that all Boolean functions of n variables can be computed by a VLSI circuit of O(2n) area and period 1, and we prove that there exist Boolean functions of n variables for which every (convex) VLSI chip must have Ω(2n) area.

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5. References

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Author information

Authors and Affiliations

  1. Department of Computer Science, University of Utrecht, P.O. Box 80.012, 3508 TA, Utrecht, the Netherlands

    M. R. Kramer & J. van Leeuwen

Authors
  1. M. R. Kramer
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  2. J. van Leeuwen
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Editor information

E. Börger G. Hasenjaeger D. Rödding

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© 1984 Springer-Verlag Berlin Heidelberg

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Kramer, M.R., van Leeuwen, J. (1984). The VLSI complexity of Boolean functions. In: Börger, E., Hasenjaeger, G., Rödding, D. (eds) Logic and Machines: Decision Problems and Complexity. LaM 1983. Lecture Notes in Computer Science, vol 171. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-13331-3_55

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  • DOI: https://doi.org/10.1007/3-540-13331-3_55

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-13331-5

  • Online ISBN: 978-3-540-38856-2

  • eBook Packages: Springer Book Archive

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