Problem 1. Turing machine for a given language [19 points] 10 pts Give a Turing machine that acoepts strings of finite length written in {0,1}, if and only these strings have the form L={xyzx is reversal of z and y contains twice as many 0 's as it has 18}, 9 pts Bound its runtime. Eramples of wonds: The following two words belong to L 100101000001 where x=100 is the reversal (string read from right to left) of z=001 and y=101000 contains two 1 's and four 0 's. 1100110010011 where x=11001 is the reversal of z=10011 and y=100 contains 1 and two 00 's. The word 1001000001 does not belong to L since the biggest prefix that is equal to its reversal is x=100 and z=001 and the remaining string 1000 does not have twice as many 0 's as it has 1 's