Success TrackerSuccess Tracker
Log inSign up

GATE CS 2018 Set 1 — Question 62

Go beyond PYQs with Success TrackerAI-powered personalised practice and doubt support. Unlimited practice on eligible plans; AI usage limits apply.
NAT+2 / -0HardDFAFinite Automata & Regular LanguagesTheory of ComputationClosure Properties (Regular)

Theory of Computation → Finite Automata & Regular Languages → Closure Properties (Regular)

Last updated

Question

Given a language LL, define LiL^i as follows:L0={ε}L^0 = \{\varepsilon\}Li=Li−1⋅L for all i>0L^i = L^{i-1} \cdot L \text{ for all } i > 0The order of a language LL is defined as the smallest kk such that Lk=Lk+1L^k = L^{k+1}.
Consider the language L1L_1 (over alphabet 0) accepted by the following automaton.
Finite automaton with three states over the alphabet {0}. The start state (left) is an accepting state (double circle) and goes to the middle state on input '0'. The middle state is an accepting state (double circle) and goes to the right state on input '0'. The right state (not accepting) goes back to the middle state on input '0'.
The order of L1L_1 is _____.
Your answer

Enter a number. Decimals, negative values and scientific notation are accepted.

The solution stays hidden until you check.

Continue learning with Success Tracker

A step still unclear? Work through it with support

Use Success Tracker to ask about the reasoning, then try another GATE CS question to check your understanding.

AI-powered practice· Unlimited practice on eligible plans
PYQs with solutions
Attempt available previous-year questions, then compare your reasoning with the worked solution. Coverage varies by stream.
Practice that adapts
Choose a topic, work on weaker areas and bookmark questions to revisit. Your attempts feed your progress tracking.
AI doubt support
Ask follow-up questions about a step or concept while practising, instead of stopping at the final answer.

Unlimited practice is available on eligible plans. Free practice and AI usage have limits; check the current plan allowances before choosing.

Start with a free accountView plans and allowances

This page stays readable without an account. AI responses can be wrong; check them against the solution and source material.

More questions on Finite Automata & Regular Languages

2026 Set 2 Q13Which one of the following statements is equivalent to the following assertion? Turing machine MM…2026 Set 1 Q25Consider the following grammar where SS is the start symbol, and aa and bb are terminal symbols.…2026 Set 1 Q26Let MM be a nondeterministic finite automaton (NFA) with 6 states over a finite alphabet. Which of…2026 Set 2 Q29Which of the following grammars is/are ambiguous?2026 Set 2 Q47Consider the following two finite automata D1D_1 and D2D_2. [figure] Which of the following…