Question

Let <M> be the encoding of a Turing machine as a string over ∑ = {0, 1}. Let L = {<M> | M is a Turing machine that accepts a string of length 2014}. Then L is

• A. decidable but not recursively enumerable
• B. decidable and recursively enumerable
• C. undecidable and not recursively enumerable
• D. undecidable but recursively enumerable

Answer 1

The correct option is D undecidable but recursively enumerable

Whether a TM accepts a finite length string or not is a non trivial question and hence by Rice's theorem the problem is undecidable.
But the problem however falls in recursively enumerable since the condition given is a positive condition.