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On disguised double horn functions and extensions

  • Logic I
  • Conference paper
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Book cover STACS 98 (STACS 1998)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1373))

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Abstract

As a natural restriction of disguised Horn functions (i.e., Boolean functions which become Horn after a renaming (change of polarity) of some of the variables), we consider the class C DH R of disguised double Horn functions, i.e., the functions which and whose complement are both disguised Horn. We investigate the syntactical properties of this class and relationship to other classes of Boolean functions. Moreover, we address the extension problem of partially defined Boolean functions (pdBfs) in C DH R, where a pdBf is a function defined on a subset (rather than the full set) of Boolean vectors. We show that the class C DH R coincides with the class C 1–DL of 1-decision lists, and with the intersections of several well-known classes of Boolean functions. Furthermore, polynomial time algorithms for the recognition of a function in C DH R from Horn formulas and other classes of formulas are provided, while the problem is intractable in general. We also present an algorithm for the extension problem which, properly implemented, runs in linear time.

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Author information

Authors and Affiliations

  1. Institut für Informatik, Universität Gießen, Arndtstraße 2, D-35392, Germany

    Thomas Eiter

  2. Department of Applied Mathematics and Physics, Graduate School of Engineering, Kyoto University, 606, Kyoto, Japan

    Toshihide Ibaraki

  3. Department of Systems and Human Science, Graduate School of Engineering Science, Osaka University, 560, Toyonaka, Osaka, Japan

    Kazuhisa Makino

Authors
  1. Thomas Eiter
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  2. Toshihide Ibaraki
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  3. Kazuhisa Makino
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Editor information

Michel Morvan Christoph Meinel Daniel Krob

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© 1998 Springer-Verlag

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Eiter, T., Ibaraki, T., Makino, K. (1998). On disguised double horn functions and extensions. In: Morvan, M., Meinel, C., Krob, D. (eds) STACS 98. STACS 1998. Lecture Notes in Computer Science, vol 1373. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0028548

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  • DOI: https://doi.org/10.1007/BFb0028548

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-64230-5

  • Online ISBN: 978-3-540-69705-3

  • eBook Packages: Springer Book Archive

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