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\title{\bf Assignment 5 \\[2ex]
\rm\normalsize CS 581 \\ Due November 20, 2018}
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\paragraph{Problem 1 [10 point]}
Show that the Complexity Class $P$ is closed under the Kleene star operation.
(Hint: Use dynamic programming. On input $y=y_1...y_n$ for $y_i \in \Sigma$,
build a table indicating for each $i \leq j$ whether the substring $y_i...y_j \in A^*$
for any $A \in P$.)

\paragraph{Problem 2 [10 point]}
State the Travelling Salesman problem as a decision problem and show that it
is an element of $NP$. (Note that the optimization version of TSP is not an element of $NP$)

\paragraph{Problem 3 [10 point]}
Show that the Complexity Class $NP$ is closed under concatenation.

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