On adequate sets of multi-valued logic. Issue 13 (September 2021) - Cheng, Daizhan; Feng, Jun-e; Zhao, Jianli; Fu, Shihua
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 .