ok, 1^3^n means Turing machine that accepts strings of 1’s of length 3n.
For every multiples of 3, the string should accept and for remaning lengths which are not divisible by 3 are should not accept. It is a easy one. Please check.

Construct a Turing machine with one tape, that accepts the language {02n1n: n ≥ 0}. Assume that, at the start of the computation, the tape head is on the leftmost symbol of the input string.
Describe a Turing machine that decides L5 = {0^3^n |n ∈ N} – the language consisting of all strings of zeroes whose length is a power of 3.
(a) Turing Machines can easily be designed to recognize regular languages. Construct either a Turing Machine that accepts the language denoted by the regular expression 0^*1 for the alphabet Σ = {0, 1}. Choose a random string in the language and trace through it (step by step) using your machine
theory of computing
3. Let x be a positive integer represented in unary form. Construct a Turing machine to compute the function fx)-3x (replace the input by function value in unary form (e.g. qo 11 1) Design a grammar for L-(a b cho,n>o).
3. Let x be a positive integer represented in unary form. Construct a Turing machine to compute the function fx)-3x (replace the input by function value in unary form (e.g. qo 11 1) Design a grammar for...
Let L = {0^n 1^n | n ≥ 0}. Draw the state diagram of a Turing
machine deciding L= Σ∗\L(basically the complement of L), where Σ =
{0,1}, and Γ = {0,1,#,U}, and “\” is set subtraction.
I understand that the complement of L will be {0^n 1^m | n=!m} U
{(0 U 1)* 1 0 {0 U 1)*}.
How should I draw the state diagram with this?
Let L = {0"1" | n > 0}. Draw the state diagram...
Let h(n) =1 if n codes a Turing machine M which halts when started on a blank tape, h(n) =0 otherwise. Sketch a proof that h is not Turing computable.
Design a DPDA M as a two-tape turing machine such that L(M) = {anbn : n>=0}
Construct a Turing machine with input alphabet {?, ?}, which accepts strings of even length.
Construct a Turing machine with input alphabet {?, ?}, which accepts strings with the same number of a’s and b’s.
construct a turing machine to compute x-y where x and y are natural numbers