Volume 4, Issue 1 (May 2009)                   IJMSI 2009, 4(1): 79-98 | Back to browse issues page



DOI: 10.7508/ijmsi.2009.01.007

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M. Golmohamadian, M. M. Zahedi. BCK-ALGEBRAS AND HYPER BCK-ALGEBRAS INDUCED BY A DETERMINISTIC FINITE AUTOMATON. IJMSI. 2009; 4 (1) :79-98
URL: http://ijmsi.ir/article-1-64-en.html

Abstract:  

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 BCKalgebra 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.

Type of Study: Research | Subject: General

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