Please generate solutions to each of the following Turing machine problems.

1. The alphabet is 0,1,null. Input is (0+1)^* Generate a single tape Turing machine that if the substring 000 is found the entire tape is erased and the machine accepts. Otherwise the machine should go to a fail state. Be sure to actually have that fail state, do not just let it halt.

2. This is a two-tape problem, the alphabet is 0,1,A,B,C,D,null. The input is on tape 1 and consists of (00+01+10+11)^* as these tuples are read AND erased if the substring 00 occurs then print A to tape 2. If 01 occurs print B, if 10 occurs print C and if 11 occurs print D. Accept when tape 1 is blank.

3. The alphabet is a, b, x and null. x will not appear as input and Null strings are allowed. If the input string is not Null and it begins with a then all a characters except that first one are erased and the output will be ab^*. If the input string begins with b then all the b characters will be erased except the first and the output will be ba^*.

4. The alphabet is a,b,c, and null. The input is (a+b+c)⁺ the output should be a mirror reflection of the input. For example if the input is aabccc then the output should be cccbaa.