GATE CS 2026 Set 1 Q.26: Regular Expressions, Finite Automata and Regular Languages

Let $M$ be a nondeterministic finite automaton (NFA) with 6 states over a finite alphabet.

Which of the following options CANNOT be the number of states in the minimal deterministic finite automaton (DFA) that is equivalent to $M$ ?

128

Official answer and solution

Official answer: B and D
From: Official GATE 2026 answer key

Solution

Apply the $2^n$ upper bound from the subset construction on an $n$ -state NFA.

By the subset construction, any NFA with $n$ states has an equivalent DFA with at most $2^n$ states, so the minimal equivalent DFA has between $1$ and $2^n$ states. For $n = 6$ , the maximum possible number of states in the minimal equivalent DFA is $2^6 = 64$ . Therefore, $65$ and $128$ (which exceed $64$ ) CANNOT be the number of states.

Final answer

Options (B), (D)

The answer is the one in the official GATE answer key. The solution is this site's own explanation.

Source

Paper: GATE 2026 Computer Science and Information Technology - Session 1 (CS1)
Question: 26 of 65
Section: Computer Science and Information Technology

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