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I'm not sure what you are asking, can you rephrase it maybe? I'm in an automata theory class so I might be able to help you, but I'm not that smart so maybe not.
Are you asking for an algorithm that given a DFA and a state of that DFA, that tells you the input(s) that get you to that state?
If that is what you are asking, then wouldn't the answer simply be to make the state you want to get to the only final state and have the resulting DFA be the machine that accepts valid inputs?
I guess I just don't know what you mean by conditions.
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