Directions: Number of points for each problem is given is square brackets. KT below in every $HW$ after that means

our main textbook Kleinberg, Tardos $($KT$).$ AB means supplemental textbook Arora, Barak.

$[2]$ Give a Turing machine $M$ such that

i$.$ its input alphabet is $0,1$ ;

ii$.,M$ accepts an input string $s$ if and only if $s$ contains twice as many $0$ s as it contains $1s.$

What is the runtime of your TM$?$

You can define $M$ either by the table of its transition function, or by a labeled graph, or by giving precise

description of its operation in plain English.