csci3255 HW 8

# csci3255 HW 8 - Section 8.1 3 Show that L = cfw_wwRw w...

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Section 8.1 3. Show that L = { ww R w : w { a , b }*} is not a context-free language. Proof: If L is context-free, then the Pumping Lemma (for context-free languages) would apply. Let m be the "magic number" cited in the Pumping Lemma. Consider the string w = ba m bba m bba m b . Clearly w L and | w | > m. Therefore, according to the Pumping Lemma, w can be written as uvxyz , with | vxy | < m and | vy | > 0, so that uv i wx i z is in L for all values of i > 0. In order to maintain that uv i wx i z is in L , we would have to pump all three groups of a 's simultaneously. But note that there is no way for vxy to span all three groups of a 's because it is shorter than m and each group of a 's is of length m . When we pump on any group of a 's, either the middle group or another group will not be pumped, violating the fact that the groups represent the same string or that string reversed. Additionally, if vxy is merely either b or bb , then it is not long enough to reach the other group of b' s, once again creating a string that does not belong to L . This is true no matter how we choose our strings. Therefore, the Pumping Lemma does not apply and L is not context-free. 7. Show that the following languages on Σ = { a , b , c } are not context-free. c)

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## This note was uploaded on 05/07/2010 for the course COMPUTER S 138 taught by Professor Icamarra during the Spring '10 term at UCLA.

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csci3255 HW 8 - Section 8.1 3 Show that L = cfw_wwRw w...

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