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Finite Definition of Languages problem

  1. May 28, 2012 #1
    1. The problem statement, all variables and given/known data
    A palindrome over an alphabet Ʃ is a string in Ʃ* that is spelled the same forward and backward. The set of palindromes over Ʃ can be defined recursively as follows:

    i) Basis: λ and a, for all a that are elements of Ʃ, are palindromes.

    ii) Recursive step: If w is a palindrome and a is an element of Ʃ, then awa is a palindrome.

    iii) Closure: w is a palindrome only if it can be obtained form the basis elements by a finite number of applications of the recursive step.

    The set of palindromes can also be defined by {w | w = w^R }. Prove that these two definitions generate the same set.

    (w^R means the reversal of w)

    2. Relevant equations

    3. The attempt at a solution
    I don't have an attempt because I'm not sure how to start the proof. Do I prove this the same way I would prove the associative law of sets, or would I prove this using induction?
  2. jcsd
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