CSE $6020$ Question $2.$ Draw the state diagram for M $,$ a Turing machine that recognizes the language $\backslash (\backslash$mathrm$\{$A$\}=\backslash$left$\backslash \{(00)^\{\backslash$mathrm$\{$n$\}\}\backslash$mid $\backslash$mathrm$\{$n$\}>0\backslash$right$\backslash \}\backslash )$ consisting of all strings of $0$ s whose length is a power of $2.$

The following is a description of what M does:

Given input string w on the tape:

$1.$ Sweep left to right across the tape, crossing off every other $0$

$2.$ If the tape contains a single $0,$ accept and halt

$3.$ If the tape contains more than a single $0$ and the number of $0$ s was odd, reject and halt

$4.$ Return the head to the left hand $($start$)$ of the tape

$5.$ Go to step $1$