Function of One Regular Separable Relation Set Decided for the Minimal Covering in Multiple Valued Logic
1 Key Lab of Knowledge Processing and Networked Manufacturing, Xiangtan, Hunan, 411105, China
2 Hunan University of Science and Technology, Xiangtan, Hunan, 411105, China
3 School of Computer & Information Engineering, HunanUniversity of Commerce, Changsha, 410250, China
4 School of Science, Qilu University of Technology, Jinan 250353, China
a Corresponding author: email@example.com Tel.: +8618573206768, +8615910080626
Multiple-valued logic is an important branch of the computer science and technology. Multiple-valued logic studies the theory, multiple-valued circuit & multiple-valued system, and the applications of multiple-valued logic included.In the theory of multiple-valued logic, one primary and important problem is the completeness of function sets, which can be solved depending on the decision for all the precomplete sets(also called maximal closed sets) of K-valued function sets noted by PK*, and another is the decision for Sheffer function, which can be totally solved by picking out all of the minimal covering of the precomplete sets. In the function structure theory of multi-logic, decision on Sheffer function is an important role. It contains structure and decision of full multi-logic and partial multi-logic. Its decision is closely related to decision of completeness of function which can be done by deciding the minimal covering of full multi-logic and partial-logic. By theory of completeness of partial multi-logic, we prove that function of one regular separable relation is not minimal covering of PK* under the condition of m = 2, σ = e.
Key words: Regular Separable Relation / Sheffer Function / Minimal Covering / Maximal Closed Set
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