NDLI: Enumeration of function and bases of three-valued set logic under compositions with Boolean functions

Content Provider	IEEE Xplore Digital Library
Author	Demetrovics, J. Reischer, C. Simovici, D. Stojmenovic, I.
Copyright Year	1994
Description	Author affiliation: Comput. & Autom. Inst., Hungarian Acad. of Sci., Budapest, Hungary (Demetrovics, J.)
Abstract	This paper discusses some classification and enumeration problems in r-valued set logic, which is the logic of functions mapping n-tuples of subsets into subsets over r values. Boolean functions are convenient choice as building blocks in the design of set logic functions. Weak maximal sets are these containing all Boolean functions. The authors give the number of n-ary functions in each weak maximal set and and some properties of intersections of weak maximal sets in r-valued set logic. These properties are used to classify all three-valued set logic functions according to the weak maximal sets they belong to. They prove that there are 29 such classes of functions and give a unary function representative for each of them. Finally, they find the number of n-ary weak Sheffer functions of three-valued set logic, i.e. functions which are complete under compositions with Boolean functions.
Starting Page	164
Ending Page	171
File Size	763187
Page Count	8
File Format	PDF
ISBN	0818656506
DOI	10.1109/ISMVL.1994.302205
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	1994-05-25
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Boolean functions Biology computing Automation Biochemistry Mathematics Computer science Logic functions
Content Type	Text
Resource Type	Article

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