Can a Finite Automata exist without any final state?

Question

It doesn't make sense to construct a language acceptor which does not able to accept any language. I specifically talking about FA which accept languages not transducer or translator which translate languages.

score 1 · Answer 1 · answered Oct 08 '16 at 07:55

People build them all the time. You have a set of states, and each state is accessible ultimately from every other, and there is no final state, so it never halts, though it might get stuck in a cycling loop. No issue with that at all.

Do a search on "busy beaver".

score 1 · Answer 2 · answered Oct 08 '16 at 08:16

The mathematical model of a FSM, as described on the wikipedia page, notes that the set F of final states may be empty. While an empty set of final states isn't much use if the FSM is used as a recogniser, FSMs can also be used as transducers.

For example, a Mealy machine doesn't include a set of final states, since it the output from the machine as the input is processed which is of interest.

score 0 · Accepted Answer · answered Oct 09 '16 at 08:41

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It is not just that it can exist - it is even necessary: how else would one accept the empty set, which is one of the regular languages. Unless you use an automaton with unaccessible states, which is pretty similar to not having a final state.

answered Oct 09 '16 at 08:41

Peter Leupold

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Thanks, I never think of empty set as a case. – lifeisshubh Oct 10 '16 at 04:41
Well, it is not the most useful case - but many times mathematically necessary according to the definitions. – Peter Leupold Oct 10 '16 at 07:45

Can a Finite Automata exist without any final state?

3 Answers3