Let L be a regular language. Consider the constructions on L below: repeat (L)…
2006
Let L be a regular language. Consider the constructions on L below: repeat (L) = {ww | w ∊ L} prefix (L) = {u | ∃v : uv ∊ L} suffix (L) = {v | ∃u uv ∊ L} half (L) = {u | ∃v : | v | = | u | and uv ∊ L} Which choice of L is best suited to support your answer above?
- A.
(a + b)*
- B.
{ϵ, a, ab, bab}
- C.
(ab)*
- D.
{anbn | n ≥ 0}
Attempted by 17 students.
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Correct answer: A
The language (a + b)* is regular and closed under the operations repeat, prefix, suffix, and half. It includes all possible strings over {a, b}, making it ideal for demonstrating closure properties of regular languages. Other options may be non-regular or too restrictive, so (a + b)* is the best choice.