# If a DFA can be simulated by a real program, can it be simulated by a TM

In proofs of decidability, we often want to simulate another model of computation by a Turing machine. But if I can simulate a $\mathsf{DFA}$ by, say, a C program, then is there some result which says that the $\mathsf{DFA}$ can be simulated by some $\mathsf{TM}$? Could a program be used in place of a $\mathsf{TM}$ in a proof of decidability?

I know that Java being Turing-complete would mean that it can simulate any $\mathsf{TM}$, so this is sort of the reverse of Turing-completeness I guess.

• Yes, of course. – Karolis Juodelė Mar 29 '14 at 20:10