###### Question 10303 – Theory-of-Computation

March 6, 2024###### Question 7809 – Operating-Systems

March 6, 2024# Question 10323 – Theory-of-Computation

(a) Given a set

S = {x| there is an x-block of 5’s in the decimal expansion of π}

(Note: x-block is a maximal block of x successive 5’s)

Which of the following statements is true with respect to S? No reasons need to be given for the answer.

- (i) S is regular

(ii) S is recursively enumerable

(iii) S is not recursively enumerable

(iv) S is recursive

(b) Given that a language L_{1} is regular and that the language L_{1} ∪ L_{2} is regular, is the language L_{2} always regular? Prove your answer.

Correct Answer: A

Theory Explanation.

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