We$$ve shown that the language L$2=\{$a$^$n b$^$n c$^$n $|$ n in Natural number$\}$ is not context$-$free and therefore cannot be recognized by a pushdown automaton $($nor by a finite automaton$).$ However, it can be recognized by a Turing machine!

a$.$ Give a high$-$level description of a Turing machine whose language is L$2$

b$.$ Draw a state$-$transition diagram for a Turing machine for L$2$ that works in the way

you described in part a$.$