Your task
A Turing machine

For this problem you are to design a Turing machine that doubles a number expressed in unary (base 1). The input to the Turing machine is given as a tape that contains a * symbol in the leftmost cell, followed by n 1 symbols in the next n cells, and then 0 symbols in the remaining (infinitely many) cells. The head of the Turing machine starts on top of the * symbol. When the Turing machine halts, the tape should contain the * symbol in its original location, followed by 2n 1 symbols in the next 2n cells, and 0 symbols in all other cells. At the end, you may leave the head of the Turing machine wherever is convenient.

Give a state transition table (similar to Figure 11.3 on page 459 of Brookshear) for this Turing machine.

Hint: you can use additional symbols besides 0, 1, and * if you need to, as long as you only use a fixed number.
P vs NP

Do problems 37 and 39 from page 492 of Brookshear.
Submitting your solutions

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Solution:
A Turing machine

Basic idea: we'll copy all the ones one at a time, marking each one that has been copied already by changing it to an x and each copy by making it a y. Then at the end we will go back and change all the symbols to ones again.
Current state	Current symbol	Write	Move	New state
START		*		*	Right	GET1
GET1	0	0	None	HALT
GET1	1	x	Right	DROP1
GET1	y	1	Right	CHANGEY
DROP1	0	y	Left	FINDX
DROP1	1	1	Right	DROP1
DROP1	y	y	Right	DROP1
FINDX	1	1	Left	FINDX
FINDX	y	y	Left	FINDX
FINDX	x	x	Right	GET1
CHANGEY	0	0	Left	CHANGEX
CHANGEY	y	1	Right	CHANGEY
CHANGEX	1	1	Left	CHANGEX
CHANGEX	x	1	Left	CHANGEX
CHANGEX	*	*	None	HALT