On disguised double horn functions and extensions

  • Thomas Eiter
  • Toshihide Ibaraki
  • Kazuhisa Makino
Logic I
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1373)

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 CDHR 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 CDHR, where a pdBf is a function defined on a subset (rather than the full set) of Boolean vectors. We show that the class CDHR coincides with the class C1–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 CDHR 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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Copyright information

© Springer-Verlag 1998

Authors and Affiliations

  • Thomas Eiter
    • 1
  • Toshihide Ibaraki
    • 2
  • Kazuhisa Makino
    • 3
  1. 1.Institut für InformatikUniversität GießenGermany
  2. 2.Department of Applied Mathematics and Physics, Graduate School of EngineeringKyoto UniversityKyotoJapan
  3. 3.Department of Systems and Human Science, Graduate School of Engineering ScienceOsaka UniversityToyonaka, OsakaJapan

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