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\title{\bf Assignment 4 \\[2ex]
\rm\normalsize CS 581 \\ Due November 1, 2018}
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\paragraph{Problem 1 [10 point]}
Consider the problem of determining whether a single-tape Turing Machine ever writes a blank symbol
over a nonblank symbol during the course of its computation on any input string. Formulate this
problem as a language and show that it is undecidable.

\paragraph{Problem 2 [10 point]}
Prove that there exists an undecidable subset of $\{1\}^*$.

\paragraph{Problem 3 [10 point]}
Prove that the following language is recognizable.
\[ \{ \langle M \rangle \;|\; M \text{ is a TM that accepts at least on element of } \{1\}^*  \} \]

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