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Michael Sipser Edition 3 Exercise 1 Question 70 (Page No. 93)

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We define the $\text{avoids}$ operation for languages $A$ and $B$ to be $\text{A avoids B = {w| w ∈ A and w doesn’t contain any string in B as a substring}.}$ Prove that the class of regular languages is closed under the ${avoids}$ operation.
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admin asked Apr 30, 2019
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Michael Sipser Edition 3 Exercise 1 Question 71 (Page No. 93)
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admin asked Apr 30, 2019
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Michael Sipser Edition 3 Exercise 1 Question 69 (Page No. 93)
Let $\sum=\{0,1\}.$ Let $WW_{k}=\{ww|w\in \sum^{*}$ and $w$ is of length $k\}.$ Show that for each $k,$ no DFA can recognize $WW_{k}$ with fewer than $2^{k}$ states. Describe a much smaller $NFA$ for $\overline{WW_{k}},$ the complement of $WW_{k}.$
Let $\sum=\{0,1\}.$ Let $WW_{k}=\{ww|w\in \sum^{*}$ and $w$ is of length $k\}.$Show that for each $k,$ no DFA can recognize $WW_{k}$ with fewer than $2^{k}$ states.Descri...
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