Let P be a regular language and Q be a context-free language such that Q ⊆ P. Then which of the following is always regular?

Question

Let a Non-deterministic Finite Automaton (NFA) have 6 states over a finite alphabet. Which of the following cannot be the number of states in a minimal Deterministic Finite Automaton (DFA) that is equivalent to this NFA?

Answer 1

The intersection of a regular language P with any language, including a context-free language Q, is always regular. This is due to regular languages being closed under intersection with other languages. Therefore, P ∩ Q will consistently be a regular language.

LIST I	LIST II
(A) Unification	(I) Variable can be done with a constant, another variable, or a function.
(B) Deep backtracking	(II) The entire conjunctive goal is executed.
(C) Forward movement	(III) Choose subgoal with possible unifier.
(D) Shallow backtracking	(IV) Previous subgoal to find alternative solutions.

Let P be a regular language and Q be a context-free language such that Q ⊆ P. Then which of the following is always regular?

Show Hint

The Correct Option is A

Solution and Explanation

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