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Peter Linz Edition 5 Exercise 9.3 Question 1 (Page No. 248)
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Consider the set of machine language instructions for a computer of your choice. Sketch how the various instructions in this set could be carried out by a Turing machine.
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Peter Linz Edition 5 Exercise 9.1 Question 1 (Page No. 238)
Write a Turing machine simulator in some higher-level programming language. Such a simulator should accept as input the description of any Turing machine, together with an initial configuration, and should produce as output the result of the computation.
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Peter Linz Edition 5 Exercise 11.3 Question 1 (Page No. 296)
Find the context-sensitive grammars for the following languages. $\text{(a)}$ $L=\{a^{n+1}b^nc^{n-1} : n\geq 1\}$. $\text{(b)}$ $L=\{a^{n}b^nc^{2n} : n\geq 1\}$. $\text{(c)}$ $L=\{a^{n}b^mc^{n}d^m : n\geq 1, m\geq1\}$. $\text{(d)}$ $L=\{ww : w\in \{a,b\}^+\}$. $\text{(e)}$ $L=\{a^{n}b^nc^{n}d^m : n\geq 1\}$.
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Peter Linz Edition 5 Exercise 11.3 Question 2 (Page No. 296)
Find context-sensitive grammars for the following languages. $(a)$ $L=\{w: n_a(w) = n_b(w) = n_c(w)\}$. $(b)$ $L=\{w: n_a(w) = n_b(w) < n_c(w)\}$.
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Peter Linz Edition 5 Exercise 10.2 Question 6,7 (Page No. 264)
Exercise 6: Show that for every Turing machine there exists an equivalent standard Turing machine with no more than six states. Exercise 7: Reduce the number of required states in Exercise 6 above as far as you can (Hint: The smallest possible number is three)
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