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Try these questions from our free AMCAT practice tests. The correct answer and an explanation follow each question.
Which of the following operations on context-free languages does NOT always produce a context-free language?
Answer: C. Intersection of two context-free languages
Context-free languages are closed under union, concatenation, and Kleene star. However, they are NOT closed under intersection. A classic example: L1 = {a^n b^n c^m} and L2 = {a^m b^n c^n} are both context-free, but L1 โฉ L2 = {a^n b^n c^n} is not context-free.
In the Chomsky hierarchy, which type of grammar generates context-free languages?
Answer: C. Type 2
The Chomsky hierarchy classifies grammars into four types: Type 0 (unrestricted/recursively enumerable), Type 1 (context-sensitive), Type 2 (context-free), and Type 3 (regular). Context-free grammars (Type 2) have rules of the form A โ ฮฑ where A is a single non-terminal.
What is an abstract class in object-oriented programming?
Answer: C. A class that cannot be instantiated and may contain abstract methods
An abstract class serves as a blueprint for other classes; it cannot be instantiated on its own and may define abstract methods that subclasses must implement.
Which of the following is true about the Pumping Lemma for regular languages?
Answer: B. It can be used to prove that a language is NOT regular
The Pumping Lemma for regular languages provides a necessary condition for regularity. If a language fails to satisfy the Pumping Lemma, it is provably NOT regular. However, satisfying the lemma does not guarantee regularity, so it cannot prove a language IS regular.