Question
Download Solution PDFWhich of the following problem is decidable for recursive language (L)?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
Decidable language: A language is decidable if there exists a Turing machine which halts or accepts it.
Explanation:
A recursive language L is given.
Statement 1: Is L = ф?
This is emptiness property. Recursive languages are not decidable for emptiness problem. Problem whether a recursive language is empty cannot be solved.
Statement 2: Is w ∈ L, where w is a string?
It means membership property of recursive language. Recursive languages are decidable for membership property. If any string is in the language than either it halts in final state or accepted by Turing machine. So, it is decidable.
Statement 3: Is L = R, where R is given regular set?
Whether a recursive language is regular, is undecidable.
Statement 4: Is L = Σ*?
As, language is decidable when there is Turing machine which halts in final state. There no algorithm which can decide this property of recursive language. So, it is undecidable.Last updated on Jul 7, 2025
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