TY - JOUR
T1 - BCK-ALGEBRAS AND HYPER BCK-ALGEBRAS INDUCED BY A DETERMINISTIC FINITE AUTOMATON
TT -
JF - IJMSI
JO - IJMSI
VL - 4
IS - 1
UR - http://ijmsi.ir/article-1-64-en.html
Y1 - 2009
SP - 79
EP - 98
N2 - 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.
M3 10.7508/ijmsi.2009.01.007
ER -