Final exam practice problems: Create TM for the following languages. assume that n $>=0$

$1.$ anbn$+1$

$2.0$n$12$n$+1$

$3.$ anb$3$n$+2$

$4.$ aanbbbncn

$5.$ aibj$,$ i $$ j $=2$ or i $=2$j $+2,$ i $>=2$ and j $>=0$

$6.$ design a Turing machine for odd numbers of $01,$ L $=\{000111110101,01,01000001111101,...\}$

$7.$ design a Turing machine for even number of $0,$ L $=\{00,0000,000000,$ epsilon$\}$

$8.$ Design a Turing machine for even number of $0$ and odd number of $1.$ L $=\{01110,1,111,00001,...\}$

$9.$ Design a Turing machine to do the subtraction such as $3-2.$ Refer to the lecture.

$10.$ review all the problems solved during the lecture

$11.$ solve the above problems using multi$-$tape Turing machine