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Show that languages are regular

  1. Dec 14, 2013 #1
    Show that languages are regular!!!

    1. The problem statement, all variables and given/known data
    Use the lemma:
    <<If the language L(A) of an automaton A has an infinite number of words,then there are words a,m,t ε Σ*,so that |at|≤|Σ_{k}|,and each word a m^{i}t,i≥0 is contained in L(A) >>(version of Pumping Lemma)and show that the following languages are not regular:
    a) L={ww^{R}:w ε {a,b}*} (w^{R}=the word w is written backwards)
    b)L={ww:w ε {a,b}*}

    P.S: Σ_{k} is the set of states.

    2. The attempt at a solution

    For the subquestion b,if we would have the original version of Pumping Lemma,we could take the word 0^{p}10^{p}1,where p is the pumping length.Can we also do this in our case?
  2. jcsd
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