HYPER K-ALGEBRAS INDUCED BY A DETERMINISTIC FINITE AUTOMATON

Abstract

In this note first we define a hyper K-algebra S on the states of a deterministic ¯nite automaton. Thenwe obtain some commutative  hyper K-ideals of types 3, 4, 5, 6 and 9 and also positive implicative hyper K-ideals of types 1, 2, 3, 4, 5, 6, 7, 8 and 9 of S. Also we prove some theorems and obtain some results, to show that some properties of this hyper K-algebra. Then we define another hyper K-algebra on the states of a deterministic finite automaton which is simple and normal. Finally, we introduce a hyper K-algebra on the set of all equivalence classes of an equivalence relation on states.