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Peter Linz Edition 5 Exercise 10.2 Question 9 (Page No. 264)
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Show that every computation that can be done by a standard Turing machine can be done a multitape machine with a stay option and at most two states.
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Peter Linz Edition 5 Exercise 10.2 Question 8 (Page No. 264)
A counter is a stack with an alphabet of exactly two symbols a stack start symbol and a counter symbol. Only the counter symbol can be put on the stack or removed from it. A $\text{counter automaton}$ is a ... one or more counters as storage. Show that any Turing machines can be simulated using a counter automaton with four counters.
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Peter Linz Edition 5 Exercise 10.2 Question 4 (Page No. 264)
Give a formal definition of a Turing machine with a single tape but multiple control units, each with a single read-write head. Show how such a machine can be simulated with a multitape machine.
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Peter Linz Edition 5 Exercise 10.2 Question 3 (Page No. 264)
Give a formal definition of a multihead-multitape Turing machine. Then show how such a machine can be simulated by a standard Turing machine.
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Peter Linz Edition 5 Exercise 10.4 Question 9 (Page No. 273)
Show that the Cartesian product of a finite number of countable sets is countable.
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