Pynko, AP |

Dopov. Nac. akad. nauk Ukr. 2017, 3:18-21 |

https://doi.org/10.15407/dopovidi2017.03.018 |

Section: Information Science and Cybernetics |

Language: Russian |

Abstract: A Boolean function is said to be partially monotonic provided it is monotonic with respect to some of its arguments, while anti-monotonic with respect to others. We argue that the conjunctive normal forms of partially monotonic Boolean functions can be minimized in a quite effective way with involving just disjuncts possesing the same partial monotonicity. |

Keywords: Boolean function, conjunct, conjunctive normal form, disjunct, disjunctive normal form, literal |

References:

- Yablonskiy, S. V. (1986). Introduction to discrete mathematics. Moscow: Nauka (in Russian).
- Quine, W.V. (1959). On cores and prime implicants of truth functions, American Math. Monthly, 66, No. 9, pp. 755-760.
- Pynko, A.P. Minimal sequent calculi for monotonic chain finitely-valued logics. Bulletin of the Section of Logic, 2014, 43, No. 1/2, pp. 99-112.
- Kapitonova, J.V., Kryvyj, S.L., Letichevskij, O.A., Luckij, G.M., & Pechurin, M.K. (2000). Foundations of discrete mathematics (in 2 volumes), Kiev: LitSoft (vol. 1: Mathematical foundations) (In Ukrainian).