Which statement is equivalent to: Turing machine M decides language L ⊆ {0,1}*

2026

Which statement is equivalent to:
Turing machine M decides language L ⊆ {0,1}*

  1. A.

    Turing machine 𝑀 halts on all input strings in {0,1}

  2. B.

    Turing machine 𝑀 accepts all input strings in L

  3. C.

    Turing machine 𝑀 rejects all input strings in {0,1}−L

  4. D.

    Turing machine 𝑀 accepts all input strings in 𝐿 and rejects all input strings in {0,1} − 𝐿

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Correct answer: D

A Turing machine M decides a language L if it satisfies two main conditions for every input string w.

First, M must halt on all inputs, meaning it never enters an infinite loop.

Second, M must accept w if w is in L, and reject w if w is not in L.

This combination ensures that for any input, the machine provides a definitive decision (accept or reject) in finite time.

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