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International Symposium on Fundamentals of Computation Theory

FCT 2001: Fundamentals of Computation Theory pp 424–427Cite as

On Logical Method for Counting Dedekind Numbers

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2138))

Abstract

A description of the property of monotonicity of Boolean functions using propositional calculus is presented, which allows to use #SAT algorithms for computing Dedekind numbers. Using an obvious modification of Davis-Putnam satisfiability algorithm, Dedekind numbers until the seventh have been calculated. Standard arithmetization of propositional logic allows to deduce Kisielewicz’s formula in more transparent way.

Supported in part by Estonian Science Foundation grant no. 3056

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References

  1. Davis, M., Putnam, H.: A computing procedure for quantification theory. J. Assoc. Comput. Mach. 7 (1960) 201–215

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  2. R. Dedekind, R.: Über Zerlegungen von Zahlen durch ihre grossten gemeinsamen Teiler. Festschrift der Technischen Hochschule zu Braunschweig bei Gelegenheit der 69 Versammlung Deutscher Naturforscher und Ärzte (1897) 1–40

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  3. Kisielewicz, A.: A solution of Dedekind’s problem on the number of isotone Boolean functions. J. reine angew. Math. 386 (1988) 139–144

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Author information

Authors and Affiliations

  1. Institute of Computer Science, University of Tartu, J. Liivi Str. 2, 50409, Tartu, Estonia

    Mati Tombak, Ain Isotamm & Tõnu Tamme

Authors
  1. Mati Tombak
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  2. Ain Isotamm
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  3. Tõnu Tamme
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Editor information

Editors and Affiliations

  1. University of Latvia, Raiņa bulvaris 29, LV-1459, Riga, Latvia

    Rūsiņš Freivalds

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© 2001 Springer-Verlag Berlin Heidelberg

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Tombak, M., Isotamm, A., Tamme, T. (2001). On Logical Method for Counting Dedekind Numbers. In: Freivalds, R. (eds) Fundamentals of Computation Theory. FCT 2001. Lecture Notes in Computer Science, vol 2138. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44669-9_48

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  • DOI: https://doi.org/10.1007/3-540-44669-9_48

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42487-1

  • Online ISBN: 978-3-540-44669-9

  • eBook Packages: Springer Book Archive

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