GATE CS 2026 Set 2 — Question 13
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Theory of Computation → Turing Machines & Computability → Recursive & RE Languages
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Question
Which one of the following statements is equivalent to the following assertion?
Turing machine decides the language
Turing machine decides the language
Correct answer
(D) Turing machine M accepts all input strings in L and rejects all input strings in \0,1\^ - L
Solution
A Turing machine is said to decide a language if and only if:
1.For every string , halts in the accept state.
2.For every string (i.e., ), halts in the reject state.
This means must halt on all inputs, accepting those in and rejecting those not in .- Option (A) only states that halts, but does not specify that it accepts exactly .
- Option (B) only states that accepts strings in , which is the definition of recognizing , but allows looping on strings not in .
- Option (C) only specifies behavior for strings not in .
- Option (D) correctly combines both conditions: accepting strings in and rejecting strings not in .
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