regular grammers ambiguity

Question

are grammars corresponding to DFA's unambiguous and those to NFA's are ambiguous? according to what I studied every DCFL is guaranteed has an unambiguous grammar though there are multiple grammars generating them every regular language is also DCFL hence they will follow the same but I doubt if every grammar corresponding to DFA is non-ambiguous and that of NFA is ambiguous

Comments

for the grammer u made both DFA and NFA are the same make a state A and define a self loop on it with symbol a and it itself is the final state so even dfa's can produce ambiguous grammers ?

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If you go for DFA then there is only one transition of a which is self-loop. But for NFA, there are two transitions going out of Q0 one is the self loop and another is to the final state.

So, Grammar of DFA is Unambiguous.

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yeah for a single alphabet as we will have atmost one transition in the machine even in the grammer we will have only one way to derive that alphabet

Answer 1

Grammar corresponding to DFA is unambiguous because we have only transition on a terminal from the state in the DFA,

ex   $a^{*}$  it have only self loop

and the grammar corresponding to the NFA  can be ambiguous  because from the same state with a terminal we can go to one or more different state

but there will be at least one unambiguous grammar for every NFA.