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  • In this short note we introduce a class of Boolean functions defined by a minimum length of its prime implicants. We show that given a DNF one can test in polynomial time whether it represents a function from this class. Moreover, in case that the answer is affirmative we present a polynomial time algorithm which outputs a shortest DNF representation of the given function. Therefore the defined class of functions is a new member of a relatively small family of classes for which the Boolean minimization problem can be solved in polynomial time. Finally, we present a generalization of the above class which is still recognizable in polynomial time, and for which the Boolean minimization problem can be approximated within a constant factor.
  • In this short note we introduce a class of Boolean functions defined by a minimum length of its prime implicants. We show that given a DNF one can test in polynomial time whether it represents a function from this class. Moreover, in case that the answer is affirmative we present a polynomial time algorithm which outputs a shortest DNF representation of the given function. Therefore the defined class of functions is a new member of a relatively small family of classes for which the Boolean minimization problem can be solved in polynomial time. Finally, we present a generalization of the above class which is still recognizable in polynomial time, and for which the Boolean minimization problem can be approximated within a constant factor. (en)
Title
  • Boolean functions with long prime implicants
  • Boolean functions with long prime implicants (en)
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  • Boolean functions with long prime implicants
  • Boolean functions with long prime implicants (en)
skos:notation
  • RIV/00216208:11320/12:10126636!RIV13-GA0-11320___
http://linked.open...avai/riv/aktivita
http://linked.open...avai/riv/aktivity
  • I, P(GAP202/10/1188)
http://linked.open...vai/riv/dodaniDat
http://linked.open...aciTvurceVysledku
http://linked.open.../riv/druhVysledku
http://linked.open...iv/duvernostUdaju
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http://linked.open...dnocenehoVysledku
  • 125382
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  • RIV/00216208:11320/12:10126636
http://linked.open...riv/jazykVysledku
http://linked.open.../riv/klicovaSlova
  • set cover; consensus method; dnf; boolean minimization (en)
http://linked.open.../riv/klicoveSlovo
http://linked.open...ontrolniKodProRIV
  • [0545C4F047FE]
http://linked.open...in/vavai/riv/obor
http://linked.open...ichTvurcuVysledku
http://linked.open...cetTvurcuVysledku
http://linked.open...vavai/riv/projekt
http://linked.open...UplatneniVysledku
http://linked.open...iv/tvurceVysledku
  • Kučera, Petr
  • Čepek, Ondřej
  • Kuřík, Stanislav
http://localhost/t...ganizacniJednotka
  • 11320
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