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CPSC 313 (6)

Non-Regular Languages

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Computer Science
Course Code
CPSC 313
Philipp Woelfel

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January 30th, 2012 Identifying Nonregular Languages We can use something called a Pumping Lemma to help us prove that certain languages are nonregular. When considering DFAs, we see that they have a bounded amount of memory. We also note that DFAs cannot accept languages where it is necessary to count arbitrary numbers. Example 3.1 Claim : The language L = fa b jn ▯ 0g over ▯ = fa;bg is not regular. Intuition : Any DFA would have to "count the number of a’s and match it with the number of b’s. Proof : Suppose there is a DFA M = (Q;▯;▯;q ;F) 0hat accepts L. Consider the states ▯ (q0;a ) for i = 0;1;2;::: ▯ n Since there is an unbounded number of i’s, but Q is
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