What is Neutrosophic Output Function

This chapter focuses on neutrosophic finite automata with output function. Some new notions on neutrosophic finite automata are established and studied, such as distinguishable, rational states, semi-inverses, and inverses. Interestingly, every state in finite automata is said to be rational when its inputs are ultimately periodic sequence that yields an ultimately periodic sequence of outputs. This concludes that any given state is rational when its corresponding sequence of states is distinguishable. Furthermore, this study is to prove that the semi-inverses of two neutrosophic finite automata are indistinguishable. Finally, the result shows that any neutrosophic finite automata and its inverse are distinguished, and then their reverse relation is also distinguished.