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L1 a m b n n 0 and m 0 and L2 a m b n b n a m n 0 and m 0 L3 L1 L2 a m b n n 0 and m 0 is also regular.

Example of non regular language. 3 Proving that picking odd-numbered symbols can create the universal set from a non-regular language. If L1 and If L2 are two regular languages their concatenation L1L2 will also be regular. This language is not regular.

Now we get that L 1 is actually every word that doesnt have lone a s inside her - which is easy to identify using. Kleene star in regular expressions or cycles in automata. Perhaps we could take n V.

Every good computer science student learns to pump it up or down in the fashion necessitated by the PL to prove sets are non-regular. Then the languages 1 L and 1 L c are also nonregular. L ab w ab.

N 0 We can argue that complement Σ -L 0 is a CFL. 0i and0j lead to the same state. This forces some kind of simple repetitive cycle within the strings.

In this section we will learn a technique for determining whether a language is regular or non-regular. 0i q 0 1i 0j-i 0i1i leads to the final state so 0j1i does also. If L were regular then since ab is regular this language would also have to be regular.

Now consider any an am S where an am. Then by the pumping lemma for context-free languages we know that w can be written. Regular languages are a subset of the set of all strings.

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