On adequate sets of multi-valued logic. Issue 13 (September 2021)

• Record Type: Journal Article
• Authors: Cheng, Daizhan; Feng, Jun-e; Zhao, Jianli; Fu, Shihua
• Is Part Of: Journal of the Franklin Institute. Volume 358:Issue 13(2021)
• Page Start: 6705
• Page End: 6722
• Publication Date: 2021-09
• Subjects: Science -- Periodicals; Technology -- Periodicals; Patents -- United States -- Periodicals; 505
• DOI: 10.1016/j.jfranklin.2021.07.003
• Languages: English
• ISSNs: 0016-0032

Abstract

Abstract: Searching a condensed adequate set of k -valued logic is a challenging problem. Using algebraic expression of logical functions, a normal form for k -valued logic was presented in Cheng et al. [3]. Starting from the normal form, searching adequate set of k -valued logic is converted to searching set of generators of their isomorphic matrix group/semigroup. Two adequate sets of k -valued logic are revealed, which consist of only 4 logical operators: one binary and three unary operators. These two adequate sets are uniformly defined for all k ≥ 3 .