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\head{CSG714}{Theory of Computation}{Spring 2009}{2 February 2009}{7}

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\Large{\bf Problem of the Week -- 4}
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\noindent {\bf Decidability and Recognizability}

Let $L$ be the following language.

\[
\{\langle M, w \rangle: M \mbox{ is a DTM and does not enter all of its
non-halting states during the computation on } w\}.
\]

Determine which of the three categories does $L$ lie in: (A)
decidable; (B) undecidable but recognizable; (c) unrecognizable.

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