Which of following problems are undecidable? I. Membership probl
Which of following problems are undecidable?
I. Membership problem in context-free languages
II. Whether a given context-free language is regular
III. Whether a finite state automation halts on all inputs
IV. Membership problem for type 0 languagesA. I and IV
B. II and IV
C. III and IV
D. I and II
Please scroll down to see the correct answer and solution guide.
Right Answer is: B
SOLUTION
Concept
A problem is said to be Decidable if we can always construct a corresponding algorithm that can answer the problem correctly. Based upon this property, problems are classified as
- Decidable
- Semi-decidable
- Undecidable
Explanation:
Statement i: Decidable
Membership problem in CFL is decidable using CYK algorithm to check the membership.
Statement ii: Undecidable
To check whether a given CFL is regular or not in undecidable.
Statement iii: Decidable
To determine whether an FA halts on all inputs or not is decidable because we have final and non-final states in FAs that indicate whether the input string is accepted or not.
Statement iv: Undecidable
Membership problem for type 0 (Recursively Enumerable) grammars is undecidable.