Let F be a family of recursively enumerable languages and let \(L_F\) \(=\{\langle M\rangle:L(M)\in…
All three conditions are required: upward closure, a finite witness for membership, and effective enumeration of finite witnesses. These conditions allow membership to be…
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Let F be a family of recursively enumerable languages and let , where M is a Turing machine. is recursively enumerable iff F satisfies which of the following conditions ?
(1) If L is in F and L ⊆ L' for some recursively enumerable language L', then L' is in F (containment property).
(2) If L is an infinite language in F, then there is a finite subset of L which is in F.
(3) The set of finite languages in F is enumerable.
Answer and explanation
Correct answer D
All three conditions are required: upward closure, a finite witness for membership, and effective enumeration of finite witnesses. These conditions allow membership to be recognized by enumerating a language until one of its finite witnesses has appeared. Upward closure and enumerability of finite members alone do not ensure that infinite members have such witnesses.
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Maharashtra and Goa SET (MH SET)