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Homework Help: Use set notation to define the language generated by the grammar

  1. Jun 4, 2012 #1
    1. The problem statement, all variables and given/known data
    As the topic states, I need to define a language, for a grammar, using set notation.

    2. Relevant equations
    Here is the grammar:
    S -> aaSB | λ
    B -> bB | b

    3. The attempt at a solution
    Okay, I know that this creates strings that are either empty or consist of an even number of 'a' characters followed by 1 or more 'b' characters.

    My first set notation is as follows:
    {(a^2m)(b^np) | m ≥ 0, n > 0, 0 < p ≤ m}
    Another variation of this I thought of but discarded (b/c I thought it would give negative exponents) is as follows:
    {(a^2m)(b^np) | m ≥ 0, n > 0, p ≤ m}

    This is a separate set notation I came up with (but I'm less confident about it):
    {(a^2m)(b^n) | m > 0, n > 0} U {(a^m)(b^m) | m = 0}

    Are either of these correct, and if not, could someone help me come up with a correct one?
  2. jcsd
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