Aspire Faculty ID #19298 · Topic: UGC NET Computer Science June 2019 (Paper II) · Just now
UGC NET Computer Science June 2019 (Paper II)

for a statement, a language $L\subseteq \Sigma^*$ is recursive if there exists some Turing machine $M$.

Which of the following conditions is satisfied for any string $\omega$?

Solution

A recursive language is decided by a Turing machine that halts on every input.

If $\omega\in L$, then the machine halts and accepts $\omega$.

If $\omega\notin L$, then the machine halts and rejects $\omega$.

Rejecting means it halts without reaching an acceptable state.

Therefore, the correct condition is:

If $\omega\notin L$, then $M$ halts without reaching an acceptable state.

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