BCK-Algebras and Hyper BCK-Algebras Induced by a Deterministic Finite Automaton

被引：6

作者：

Golmohammadian, M. ^{[1
]}

Zahedi, M. M. ^{[1
]}

机构：

[1] Tarbiat Modares Univ, Dept Math, Tehran, Iran

来源：

IRANIAN JOURNAL OF MATHEMATICAL SCIENCES AND INFORMATICS | 2009年 / 4卷 / 01期

关键词：

Deterministic finite automaton; BCK-algebra; hyper BCK-algebra; quotient BCK-algebra;

D O I：

10.7508/ijmsi.2009.01.007

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this note first we define a BCK-algebra on the states of a deterministic finite automaton. Then we show that it is a BCK-algebra with condition (S) and also it is a positive implicative BCK-algebra. Then we find some quotient BCK-algebras of it. After that we introduce a hyper BCK-algebra on the set of all equivalence classes of an equivalence relation on the states of a deterministic finite automaton and we prove that this hyper BCK-algebra is simple, strong normal and implicative. Finally we define a semi continuous deterministic finite automaton. Then we introduce a hyper BCK-algebra S on the states of this automaton and we show that S is a weak normal hyper BCK-algebra.

引用

页码：79 / 98

页数：20

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