Are DFAs unique?

Question

For a given regular is expression, once we construct a deterministic finite automaton: is that automaton unique for that expression? In a sense, that no other DFA (different number of vertices or transitions) can be constructed from that same regular expression.

score 12 · Accepted Answer · answered Dec 24 '16 at 11:47

12

For every regular language there are infinitely many DFAs accepting the language. You can always add dummy states not reachable from the initial state, for example.

However, there is a unique DFA which has the minimum number of states, called the minimal automaton (or some such name). This is part of Myhill–Nerode theory.

answered Dec 24 '16 at 11:47

Yuval Filmus

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(Unique up to isomorphism.) – reinierpost Feb 03 '17 at 09:50
How to make a state which is unreachable? Can a DFA be disconnected? – Gyanshu Apr 24 '17 at 16:14
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@Gyanshu There is absolutely no requirement in the definition of DFA that its graph be connected. – Yuval Filmus Apr 24 '17 at 16:58

Are DFAs unique?

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