Minimization of the conjunctive normal forms of partially monotonic Boolean functions

Authors

  • A.P. Pynko V.M. Glushkov Institute of Cybernetics of the NAS of Ukraine, Kiev

DOI:

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

Keywords:

Boolean function, conjunct, conjunctive normal form, disjunct, disjunctive normal form, literal

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.

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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. https://doi.org/10.2307/2310460

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).

Published

22.05.2024

How to Cite

Pynko, A. (2024). Minimization of the conjunctive normal forms of partially monotonic Boolean functions . Reports of the National Academy of Sciences of Ukraine, (3), 18–21. https://doi.org/10.15407/dopovidi2017.03.018

Issue

Section

Information Science and Cybernetics