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A Turing Machine for the language
$L=a^n b^m c^n d^m \mid n \ge 1,\ m \ge 1$ is designed.

The resultant model is

$M=({q_0,q_1,q_2,q_3,q_4,q_5,q_6,q_7,q_f},{a,b,c,d},{a,b,c,d,X_1,X_2,Y_1,Y_2},\delta,q_0,B,{q_f})$

and part of $\delta$ is given in the transition table.

You need to write the following questions based on design of Turing Machine for the given language.

Note that, while designing the Turing Machine $X_1$ and $X_2$ are used to work with $a$'s and $c$'s and $Y_1$ and $Y_2$ are used to handle $b$'s and $d$'s of the given string.


What is the Move in the cell with number 'M1' of the resultant Table ?






Solution

$M1$ is used when the machine is in state $q1$ and reads symbol $c$.

In this stage, the machine has already marked one $a$ as $X1$ and is searching for the corresponding $c$.

So, when it finds $c$, it marks it as $X2$ and moves left to return back.

Therefore,

$M1=(q2,X2,L)$



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