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Regular language vs non regular language. Two regular expressions are equivalent if languages generated by them are same. First well prove that if D is a DFA for L then when D is run on any two different strings an and am the DFA D must end in different states. Every regular language L has some some fixed number p.
If X and Y are regular then X union Y is also regular. Suppose D is a DFA for L where D ends in the same state when run on two distinct strings an and amSince D is deterministic D. A regular language is one that can be recognized by a finite machinethat is by a computer with a finite amount of memory.
A finite language is what you would expect it to be a language that can be listed in a finite amount of time. Your example is indeed a regular language. N l 0 Regular languages.
The existence of non-regular languages is guaranteed by the fact that the regular languages of any alphabet are countable and we know that the set of all subsets of strings is not countable. N l n l L a b c. 2 There are an uncountable number of languages.
For all k 0 xykz 2 L. Closure Properties of Regular Languages. Y 6 Λ.
This true because every description of a regular language is of finite length so there is a countably infinite number of such descriptions. Use the Pumping Lemma. Jxyj n.
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