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Official PYQ · 1991

GATE CS 1991 Q03 — Regular and Context-free Languages

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Which of the following is the strongest correct statement about a finite language over some finite alphabet Σ?\Sigma?

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Answer: D

A finite language LL over a finite alphabet Σ\Sigma contains a finite number of strings, say L={w1,w2,…,wk}L = \{w_1, w_2, \dots, w_k\}.

We can construct a regular expression for LL by taking the union of all its strings:

R=w1+w2+⋯+wkR = w_1 + w_2 + \dots + w_k

Since we can always write a regular expression for any finite language, every finite language is a regular language.

According to the Chomsky hierarchy, the language families are nested as follows:

Regular⊂Context-Free⊂Context-Sensitive⊂Decidable⊂Turing-Recognizable\text{Regular} \subset \text{Context-Free} \subset \text{Context-Sensitive} \subset \text{Decidable} \subset \text{Turing-Recognizable}

Thus, while statements (B), (C), and (D) are all technically true for a finite language, statement (D) ("It is a regular language") is the strongest (most specific and restrictive) correct statement because the class of regular languages is the smallest family among the options that contains all finite languages.

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