Question

Prove that the following are not regular languages. Just B and F please

Prove that the following are not regular languages. {0^n1^n | n Greaterthanorequalto 1}. This language, consisting of a string of 0's followed by an equal-length string of l's, is the language L_01 we considered informally at the beginning of the section. Here, you should apply the pumping lemma in the proof. The set of strings of balanced parentheses. These are the strings of char­acters "(" and ")" that can appear in a well-formed arithmetic expression. {0^n10^n | n Greaterthanorequalto 1}. {0^n1^m2^n | n and m are arbitrary integers}. {0^n1^m | n Greaterthanorequalto m}. {0nl2n | n lessthanorequalto 1}.

Answer 1

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4.1.3: Let n be the pumping-lemma constant (note this n is unrelated to the n that is a local variable in the definition of the language L). Pick w0n10n. Then when we write w xyz, we know that xyln, and therefore y consists of only 0's. Thus, xz, which must be in L if L is regular, consists of fewer than n 0's, followed by a 1 and exactly n O's. That string is not in L, so we contradict the assumption that L is regular.

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