Consider the grammar G with the productions: S o aSb \mid SWhich one of the following is correct?

Question

Consider the grammar G  with the productions: S 	o aSb \mid SWhich one of the following is correct?

BlackTom AI · Accepted Answer

First, let’s restate the question and the answer choices to make sure we’re evaluating the right options.
Question: Consider the grammar G with the productions: S -> aSb | S. Which statement is correct?
Options:
 a. The grammar G is a regular grammar and L(G) is not a regular language.
 b. L(G) = { a^n b^n | n >= 0 } and L(G) is not a regular language.
 c. The grammar G is a regular grammar and L(G) is a regular language.
 d. The grammar G is not a regular grammar and L(G) is a regular language.

Now, examine each option in turn.

Option a: The claim that the grammar is regular while the language is not regular.
- A regular grammar is one where all productions are of a restricted form (either A -> aB or A -> a or ε). Here, the production S -> aSb is not right-linear or left-linear; it places a nonterminal S between terminals, which cannot be captured by a regular grammar form. Therefore, the grammar is not regular. This makes option a inconsistent: it asserts regularity that doesn’t hold, so it is incorrect.

Option b: The language is L(G) = { a^n b^n | n >= 0 } and this language is not regular.
- The form a^n b^n is the classic non-regular language (proved, for example, by the pumping lemma). If the grammar (as intended) generates exactly equal numbers of a’s followed by b’s, then the language is indeed { a^n b^n | n >= 0 } and not regular. This aligns with the standard result that a^n b^n is non-regular, so this option is plausible and matches the well-known property of the language.

Option c: The grammar is regular and the language is regular.
- As discussed for option a, the grammar is not regular due to the S -> aSb production, and the language a^n b^n is not regular. Therefore, this option is false on both counts.

Option d: The grammar is not regular and the language is regular.
- While it correctly states the grammar is not regular, it incorrectly claims the language is regular. Since a^n b^n is not a regular language, this option is also false.

Putting the pieces together, the only statement that matches the established properties (non-regular language a^n b^n and a non-regular grammar form) is option b. The other options either mischaracterize the regularity of the grammar or mischaracterize the regularity of the language, or both.

Languages and Computation (COMP2049 UNNC) (SPC1 24-25) Lab Quiz 6 - Group A

Consider the grammar G with the productions: S \to aSb \mid SWhich one of the following is correct?

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