Minimization of the conjunctive normal forms of partially monotonic Boolean functions
DOI:
https://doi.org/10.15407/dopovidi2017.03.018Keywords:
Boolean function, conjunct, conjunctive normal form, disjunct, disjunctive normal form, literalAbstract
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.
Downloads
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).
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2024 Reports of the National Academy of Sciences of Ukraine

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.