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Proving NFA accepts reverse string of DFA

  1. Mar 7, 2012 #1
    I have seen descriptions for an algorithm that can take a regular deterministic finite automata and create a non-deterministic finite automata that is guaranteed to generate the reverse of string accepted by the DFA. Does anyone know of a "formal" proof that shows this is true in all cases? Guessing induction would be used to prove?

    The algorithm goes something like this:

    Take original DFA, and change the initial state to the final state
    Reverse all accepting states in DFA to non-accepting states
    Set original starting state to accepting state and reverse all transitions
    Any thoughts would be greatly appreciated!
     
  2. jcsd
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