The GATE Grind

GATE 2021 CS (CS2) – Question 46

Theory of Computation · Turing Machines and Undecidability · 2 marks · Multiple choice

S1: Every infinite regular language has an undecidable language as a subset. S2: Every finite language is regular. Which are true?

  1. S1 only
  2. S2 only
  3. Both
  4. Neither

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: (C) Both

Explanation

An infinite language has uncountably many subsets, while there are only countably many algorithms and therefore decidable languages. Thus some subset is undecidable, proving S1. Any finite language is a finite union of singleton-word regular expressions, proving S2. Both hold, C.

More Turing Machines and Undecidability questions

All Turing Machines and Undecidability questions →