My friend believes that we can convert a DFA into an equivalent PDA as follows:

Question

My friend believes that we can convert a DFA into an equivalent PDA as follows: everything remains the same as the DFA except for every transition labelled a in the DFA, we augment the transition to be a, element rightarrow elementof between the same pair of states. Is his idea correct? His idea is correct because DFAs and PDAs recognize the same class of languages. His idea is correct because DFAs are just PDAs that ignore its stack. His idea is not correct because this introduces empty transitions, which were not present in the DFA. His idea is not correct because there are some languages that a DFA can recognize that a PDA cannot. None of the above.

Explanation / Answer

my friend believes that we can convert a DFA into an equivalent PDA as follows: everything remains the same as the PDA except for every transition labelled a in the DFA, we augment the transition to be a1 e belongs e between the same pair of states:

Answer: His idea is correct because DFA and PDA recognise the same class of language.

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