Abstract

APPLICATION OF GREEN?S RELATION AND AUTOMATA THEORY ON FINITE FULL TRANSFORMATION SEMIGROUP

Kehinde R., Abdulazeez O.H. and Atteh E.M.

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The finite full transformation semigroup is the semigroup congener of the symmetric group. This class of semigroup arises naturally in automata theory. In this research work, having studied the finite full transformation semigroup in a very logical way, we have showed how the Green?s relation can be used to determine the order of any given finite full transformation semigroup and this order is given in compact form as |T_n | = ?_(r=1)^n??|J_r | ?where J_1 ,J_2 ,?,J_n ? T_n. We equally established that the automata theory can also be used to directly define elements of the full transformation semigroup. Keywords: Automata, Full Transformation, Green?s relation, Semigroup, Order.

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