Design a Turning Machine that computers the following function:

$2$For the following problems, please draw a Turing Machine that describes the

language$/$functions$.$

Design a Turing Machine that recognizes the language $a^{**}ba{b}^{**}.$ Show the sequence of

configurations of this machine when processing the string aba

Design a Turing Machine that recognizes all bit strings which do not contain the

substring $101.$ Show the sequence of configurations of this machine when processing

the string $0100.$

Given a positive integer $x$ in binary representation, design a TM that computers the

following function $($assume $x>2)$:

$f(x)=\{\begin{array}{ccc}2x,& if\text{x}\text{m}\text{o}\text{d}& 3=0\\ x,& if\text{x}\text{m}\text{o}\text{d}& 3=1\\ 2x+1,& if\text{x}\text{m}\text{o}\text{d}& 3=2\end{array}$x$,$ if x mode $3=0$