Question
Download Solution PDFConsider the following problems:
(i) Whether a finite automaton halts on all inputs?
(ii) Whether a given Context Free Language is Regular?
(iii) Whether a Turing Machine computes the product of two numbers?
Which one of the following is correct?Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFStatement i: Decidable
A language is decidable when there is a machine which halts for every string in that language and goes to non-final state for string not in the language. A finite automaton is a special case of a Turing machine which halts on all inputs that are in the language, so it is decidable.
Statement ii: Undecidable
Regular property of context free languages is undecidable. This can be proved by taking regular language as Σ*. Assume both G and R as part of input problem. For any family of languages, whether it is equal to other language is decidable if both L1 and L2 are subset of each other.
Statement iii: Undecidable
Turing machine is for recursive enumerable languages (for type 0 problems). Type 0 problems are undecidable. If we do not know about the Turing machine, it could possible that result for any two numbers will go into infinite loop and never halt. If it happens, then problem is undecidable.Last updated on Jul 7, 2025
-> The UGC NET Answer Key 2025 June was released on the official website ugcnet.nta.ac.in on 06th July 2025.
-> The UGC NET June 2025 exam will be conducted from 25th to 29th June 2025.
-> The UGC-NET exam takes place for 85 subjects, to determine the eligibility for 'Junior Research Fellowship’ and ‘Assistant Professor’ posts, as well as for PhD. admissions.
-> The exam is conducted bi-annually - in June and December cycles.
-> The exam comprises two papers - Paper I and Paper II. Paper I consists of 50 questions and Paper II consists of 100 questions.
-> The candidates who are preparing for the exam can check the UGC NET Previous Year Papers and UGC NET Test Series to boost their preparations.