Improvements of the Construction of Exact Minimal Covers of Boolean Functions

  • Bernd Steinbach
  • Christian Posthoff
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6928)


The calculation of an exact minimal cover of a Boolean function is an NP-complete problem. In this paper we introduce the definition of this problem and its basic solution. By using a slightly modified algorithm, we get a speed-up factor of more than 104. The main contributions of this paper are the description of an alternative approach mentioned in [15], and a remarkable improvement of this algorithm. In both cases operations of the XBOOLE library are used. Using the newly suggested algorithm, the time required for the calculation could be reduced by a factor of more than 8 ∗ 108 in comparison with the previous algorithm.


Boolean Function Covering Problem Unate Covering Bell System Technical Journal Negative Literal 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Bernd Steinbach
    • 1
  • Christian Posthoff
    • 2
  1. 1.Institute of Computer ScienceFreiberg University of Mining and TechnologyFreibergGermany
  2. 2.The University of The West IndiesTrinidad & TobagoJamaica

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