Title | Minimization of the conjunctive normal forms of partially monotonic Boolean functions |
Publication Type | Journal Article |
Year of Publication | 2017 |
Authors | Pynko, AP |
Abbreviated Key Title | Dopov. Nac. akad. nauk Ukr. |
DOI | 10.15407/dopovidi2017.03.018 |
Issue | 3 |
Section | Information Science and Cybernetics |
Pagination | 18-21 |
Date Published | 3/2017 |
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. 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).