%0 Journal Article
%A M. Golmohamadian,
%A M. M. Zahedi,
%T BCK-ALGEBRAS AND HYPER BCK-ALGEBRAS INDUCED BY A DETERMINISTIC FINITE AUTOMATON
%J Iranian Journal of Mathematical Sciences and Informatics
%V 4
%N 1
%U http://ijmsi.ir/article-1-64-en.html
%R 10.7508/ijmsi.2009.01.007
%D 2009
%K
%X 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.
%> http://ijmsi.ir/article-1-64-en.pdf
%P 79-98
%& 79
%!
%9 Research paper
%L A-10-1-60
%+
%G eng
%@ 1735-4463
%[ 2009