Ullman (TOC) Edition 3 Exercise 4.2 Question 11 (Page No. 149)

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Ullman (TOC) Edition 3 Exercise 4.2 Question 14 (Page No. 149 - 150)
We described the $"$product construction$"$ that took two DFA's and constructed one DFA whose language is intersection of the languages of the first two. Show how to perform the product construction on ... the product construction so the resulting DFA accepts the union of the languages of the two given DFA's.

We described the $"$product construction$"$ that took two DFA's and constructed one DFA whose language is intersection of the languages of the first two.Show how to perfo...

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Ullman (TOC) Edition 3 Exercise 4.2 Question 13 (Page No. 149)
We can use closure properties to help prove certain languages are not regular. Start with the fact that the language $L_{0n1n}=\{0^{n}1^{n}|n\geq 0\}$ is not a regular set. Prove the following languages not to be regular by transforming them using operations known to ... $\{0^{n}1^{m}2^{n-m}|n\geq m\geq 0\}$

We can use closure properties to help prove certain languages are not regular. Start with the fact that the language $L_{0n1n}=\{0^{n}1^{n}|n\geq 0\}$ is not a regular se...

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Ullman (TOC) Edition 3 Exercise 4.2 Question 12 (Page No. 149)
Let $w_{1}=a_{0}a_{0}a_{1},$ and $w_{i}=w_{i-1}w_{i-1}a_{i}$ for all $i>1.$For instance,$w_{3}=a_{0}a_{0}a_{1}a_{0}a_{0}a_{1}a_{2}a_{0}a_{0}a_{1}a_{0}a_{0}a_{1}a_{2}a_{3}.$ The shortest ... is $O(n^{2}).$ Find such an expression. Hint $:$ Find $n$ languages, each with regular expressions of length $O(n).$ Whose intersection is $L.$

Let $w_{1}=a_{0}a_{0}a_{1},$ and $w_{i}=w_{i-1}w_{i-1}a_{i}$ for all $i>1.$For instance,$w_{3}=a_{0}a_{0}a_{1}a_{0}a_{0}a_{1}a_{2}a_{0}a_{0}a_{1}a_{0}a_{0}a_{1}a_{2}a_{3}...

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Ullman (TOC) Edition 3 Exercise 4.2 Question 10 (Page No. 149)
Suppose that $L$ is any language not necessarily regular whose alphabet is $\{0\};$i.e. the strings of $L$ consist of $0's$ only. Prove that $L^{*}$ is regular. Hint$:$ At first this theorem sounds preposterous. However, an example will help you see ... use copy of $000$ and $(j-3)/2$ copies of $00.$ Thus ,$L^{*}=$ $\in + 000^{*}.$

Suppose that $L$ is any language not necessarily regular whose alphabet is $\{0\};$i.e. the strings of $L$ consist of $0's$ only. Prove that $L^{*}$ is regular. Hint$:$ A...

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Ullman (TOC) Edition 3 Exercise 4.2 Question 11 (Page No. 149)

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