Please help with this Discrete Math question Thank you in ad

Please help with this Discrete Math question. Thank you in advance!

Construct a Turing machine (your answer must show all of the 5-tuples involved) that recognizes the set {02n1n | n 1}. Include a trace of the determination that 000011 is accepted by the machine.

Solution

1)Initially it is given a finite sequence of 0’s and 1’s on its tape, preceded and followed by
an infinite number of blanks.

How would this machine proceed?

-->Starting at the left end of the input, it changes a 0 into an x. and that 0\'s are power of 2.
-->It moves to the right over whatever 0’s and y’s it sees until it comes to a 1.
-->It changes the 1 to a y .
-->It moves left over 0’s and y’s until it finds an x.
-->At this point it looks for a 0 immediately to the right, and if it finds one, changes
it into an x and repeat the process, changing a matching 1 to y.

   M= ({q0,q1,q2,q3,q4},{0,1},{0,1,x,y,^}, , q0,^,{q4})

As M performs its computation, the portion of the tape, that the head has visited will
always be a sequence of symbols described by the regular expression x*0*y*1*.

       i)Write the function .
       ii)Check that it accepts 000011
       iii)Check that it rejects 0010

Transition diagrams for Turing Machines:
   The same as for PDA a TM can be represented with a diagram.
   A transition diagram consists of:
   -->set of nodes corresponding to the states of the TM.
   -->An arc from state q to state p is labeled by one or more items of the form X/YD, where X and Y
are tape symbols, and D is a direction, either L or R. That is, whenever (q,X)=(p,Y,D), we find the
label X/YD on the arc from q to p.
   -->The start and final states representations follow the same conventions as for other kinds of
transition diagrams

Represent the transition diagram for the TM that accepts {02n1n}
-->In this our machine acceps zeros untill 1 comes after 1 i won\'t take again zero\'s.