Skip to content
GATEiit

GATE CSE 2021 Set 2 Q19: Language that always has a minimal DFA with the same k states

Question

Let L⊆{0,1}∗L \subseteq \{0,1\}^* be an arbitrary regular language accepted by a minimal DFA with kk states. Which one of the following languages must necessarily be accepted by a minimal DFA with kk states?

Try it: multiple choice: exactly one correct option

Select one option
Wrong answer costs 1/3 mark in GATE.
Show answer and explanation

Answer: C (official GATE 2021 final answer key)

Concept used: Complementing a complete DFA only swaps accepting and non-accepting states, so the number of states of the minimal DFA is unchanged.

First step: Swap final and non-final states of the minimal DFA for LL and ask whether any two states could become equivalent.

Full step-by-step solution

Detailed working, common mistakes and linked mock tests will be available with a free GATEiit account. Log-in is coming soon.

Share this question

WhatsAppDownload image

Source: official GATE 2021 Set 2 CS question paper and final answer key, organised by IIT Bombay. Question paper · Answer key

More Theory of Computation PYQs

PracticePractise Theory of Computation questions →Full paperAll GATE CSE 2021 Set 2 questions →