Question: Question 1: A language L is said to be defined if there exists a positive integer k such that, for any string w, the

Question 1: A language L is said to be defined if there exists a positive integer k such that, for any string

Question 1: A language L is said to be defined if there exists a positive integer k such that, for any string w, the membership of w in L depends solely on the last k symbols of w. (a) Provide a formal definition of this concept. (b) Prove that every defined language is regular. (c) Demonstrate that the class of defined languages is closed under unions and intersections. (d) Give an example of a defined language L such that L* is not defined. (e) Provide examples of defined languages L and L such that the concatenation L L is not defined.

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