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Peter Linz Edition 5 Exercise 12.1 Question 7,8 (Page No. 308)
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$i)$ Show that there is no algorithm for deciding if any two Turing machines $M_1$ and $M_2$ accept the same language.
$ii)$ How is the conclusion of $i$ affected if $M_2$ is a finite automaton$?$
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Peter Linz Edition 5 Exercise 12.1 Question 16 (Page No. 308)
Determine whether or not the following statements is true: Any problem whose domain is finite is decidable.
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Peter Linz Edition 5 Exercise 12.1 Question 15 (Page No. 308)
Let $\Gamma = \{0,1,\square\}$ and let $b(n)$ be the maximum number of tape cells examined by any $n-$state Turing machine that halts when started with a blank tape. Show that $b(n)$ is not computable.
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Peter Linz Edition 5 Exercise 12.1 Question 14 (Page No. 308)
Consider the set of all $n-$state Turing machines with tape alphabet $\Gamma = \{0,1,\square\}$. Give an expression for $m(n)$, the number of distinct Turing machines with this $\Gamma$.
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Peter Linz Edition 5 Exercise 12.1 Question 13 (Page No. 308)
Let $B$ be the set of all Turing machines that halt when started with a blank tape. Show that this set is recursively enumerable, but not recursive.
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