Computer Science Engineering (CSE) Exam > Computer Science Engineering (CSE) Questions > Which of the following is/are undecidable?a)G...
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Which of the following is/are undecidable?
- a)Given a TM M, decide is M accepts are strings.
- b)Given a TM, M decide is M takes more than 1073 steps on every string.
- c)Given two turing machines M1 and M2 decide of L(M1) = L(M2) .
- d)Given a TM M, decide is L(M) is regular.
Correct answer is option 'A,C,D'. Can you explain this answer?
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Which of the following is/are undecidable?a)Given a TM M, decide is M ...
For a given TM, M decide that m takes more than 1073 steps on every string is decidabe only.
Remaining are undecidable (A), (C) and (D) are undecidable.
Remaining are undecidable (A), (C) and (D) are undecidable.
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Which of the following is/are undecidable?a)Given a TM M, decide is M ...
Undecidable Problems
In theoretical computer science, there are certain problems that cannot be solved by any algorithm or Turing machine. These problems are known as undecidable problems. They are fundamental limitations in the field of computation and have significant implications for the theory of computation.
Explanation of Options
Let's go through each option to understand why it is undecidable:
Option A: Given a TM M, decide if M accepts all strings.
This problem is undecidable because it is equivalent to the Halting Problem, which states that there is no algorithm that can determine whether a given Turing machine halts on a given input. If we could decide whether a Turing machine accepts all strings, we could use that decision procedure to solve the Halting Problem, which is proven to be undecidable.
Option B: Given a TM M, decide if M takes more than 1073 steps on every string.
This problem is decidable because we can simulate the execution of the Turing machine on all possible inputs up to 1073 steps. If the Turing machine halts within this limit on any input, we can decide that it does not take more than 1073 steps on every string. Therefore, this option is not undecidable.
Option C: Given two Turing machines M1 and M2, decide if L(M1) = L(M2).
This problem is undecidable because it is equivalent to the problem of determining whether two Turing machines accept the same language. This problem is known as the equivalence problem for Turing machines and is proven to be undecidable.
Option D: Given a TM M, decide if L(M) is regular.
This problem is undecidable because it is equivalent to the problem of determining whether a given language is regular. This problem, known as the regularity problem, is proven to be undecidable.
Conclusion
In summary, options A, C, and D are undecidable problems. Option B is decidable, as it can be solved by simulating the Turing machine execution on all possible inputs up to a given step limit. The undecidability of these problems has significant implications for the limitations of computation and the theory of computation.
In theoretical computer science, there are certain problems that cannot be solved by any algorithm or Turing machine. These problems are known as undecidable problems. They are fundamental limitations in the field of computation and have significant implications for the theory of computation.
Explanation of Options
Let's go through each option to understand why it is undecidable:
Option A: Given a TM M, decide if M accepts all strings.
This problem is undecidable because it is equivalent to the Halting Problem, which states that there is no algorithm that can determine whether a given Turing machine halts on a given input. If we could decide whether a Turing machine accepts all strings, we could use that decision procedure to solve the Halting Problem, which is proven to be undecidable.
Option B: Given a TM M, decide if M takes more than 1073 steps on every string.
This problem is decidable because we can simulate the execution of the Turing machine on all possible inputs up to 1073 steps. If the Turing machine halts within this limit on any input, we can decide that it does not take more than 1073 steps on every string. Therefore, this option is not undecidable.
Option C: Given two Turing machines M1 and M2, decide if L(M1) = L(M2).
This problem is undecidable because it is equivalent to the problem of determining whether two Turing machines accept the same language. This problem is known as the equivalence problem for Turing machines and is proven to be undecidable.
Option D: Given a TM M, decide if L(M) is regular.
This problem is undecidable because it is equivalent to the problem of determining whether a given language is regular. This problem, known as the regularity problem, is proven to be undecidable.
Conclusion
In summary, options A, C, and D are undecidable problems. Option B is decidable, as it can be solved by simulating the Turing machine execution on all possible inputs up to a given step limit. The undecidability of these problems has significant implications for the limitations of computation and the theory of computation.
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Which of the following is/are undecidable?a)Given a TM M, decide is M accepts are strings.b)Given a TM, M decide is M takes more than 1073 steps on every string.c)Given two turing machines M1 and M2 decide of L(M1) = L(M2) .d)Given a TM M, decide is L(M) is regular.Correct answer is option 'A,C,D'. Can you explain this answer?
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