Problem $5.$ Iet $\backslash ($ M $\backslash )$ be the following Turing Machine

M

$\backslash \{$This problem is related to Example D in the slides from Chap $9\mathrm{.}1$ Part $1]$

a$.$ Do a configuration trace for the Turing Machine M to show that $\backslash (\backslash$mathrm$\{$w$\}=\backslash )$ aabab is accepted by M$.$ You must use the correct configuration pattem for Turing Machines.

b$.$ Does your configuration trace prove that M accepts $\backslash (\backslash$mathrm$\{$w$\}=\backslash )$ aabab? Justify your answer.

c$.$ Use JFLAP to create and test a Turing Machine M$1$ that accepts

$\backslash (\backslash$mathrm$\{$L$\}=\backslash$left$\backslash \{\backslash$mathrm$\{$w$\}\backslash$in$\backslash \{\backslash$mathrm$\{$a$\},\backslash$mathrm$\{$b$\}\backslash \}^\{*\}$: $\backslash$mathrm$\{$w$\}\backslash$right$.\backslash )$ has at least $2$ bs$\backslash (\backslash \}\backslash ).$ Do this by modifying M above. Test your new machine with the strings: aaaa, baaaab, abaabaabaa $,$ abaaaa, aaaabba $,$ b$,$ bb$.$ Submit the JFLAP diagrams for M$1$ and for the testcases for M$1.$