Construct a Mealy machine to count the number of substring $111$ in a given

binary string. The number of $1$s in output string should indicate the number of

occurrence of $111$ in the input string. Suppose the input string is $110011111101111$

$3.(10$ points$)$ Construct a Turing machine to compute f$($#w#$)=$ #wR w#$.$ Trace your machine

using w$=$#abc#