Which property of regular languages states that any sufficiently long string can be decomposed into parts to allow repetition?

• A. Pumping Lemma
• B. Closure Property
• C. Substitution Lemma
• D. Myhill-Nerode Theorem

Answer: (A)

The idea being tested is the pumping property of regular languages. Regular languages have a guarantee that any string long enough can be split into three parts, s = x y z, with |y| > 0 and |xy| ≤ p, such that for every i ≥ 0 the string x y^i z still lies in the language. This comes from the finite number of states in a DFA: a sufficiently long input must cause some state to repeat, creating a loop that you can traverse extra times without leaving the language. So the so-called pumpable section y can be repeated any number of times, and the resulting strings remain valid members of the language. This exact property is what the question describes. The other choices refer to different aspects of regular languages—how they behave under certain operations, or how they are characterized—without capturing this specific repetition feature.