DFA without final state

Question

We can have a Deterministic Finite Automata (DFA) without final state. Whether it's meant! What is the meaning of a Deterministic Finite Automata (DFA) without final state?

Thanks

Answer 1

Yes Possible. If an automata is not acceptor but transducer then final state is not needed.

Any class of an automata can be without a final state! An automata can be thought as a finite representation of a formal language(that can be infinite set). An automata with the final state(s) is called acceptor. For example, A DFA as acceptor either accepts or reject a string and represents a regular language.

But another model of automata is called transducer that may not have any final state. The purpose of automata as a transducer is to produce output string for a given input string. Example for finite state machine as transducer is Mealy and Moor machine.