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.


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.

  • 1
    $\begingroup$ (Unique up to isomorphism.) $\endgroup$ Feb 3 '17 at 9:50
  • $\begingroup$ How to make a state which is unreachable? Can a DFA be disconnected? $\endgroup$
    – Gyanshu
    Apr 24 '17 at 16:14
  • 2
    $\begingroup$ @Gyanshu There is absolutely no requirement in the definition of DFA that its graph be connected. $\endgroup$ Apr 24 '17 at 16:58

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