Construct TM that will accepts the language L = {0i0j0k/ i < j < k}

Question

How to Construct a Turing Machine that will accepts the language L = {0i0j0k/ i < j < k}.

Answer 1

I take this to mean the language 0^i 0^j 0^k | i < j < k. At least, I don't see any other obvious interpretations of it.

The shortest string in this language is obtained by taking i = 0, j = 1 and k = 2'; this yields the string 000 in the language.

Note also that all strings of more than three zeroes are also in the language since we can take i = 0, j = 1 and k = n - 1 (for n >= 3).

Our language is thus equal to 0^n | n >= 3. This language is regular. A minimal DFA for this language is as follows:

Q    s    Q'
q0   0    q1
q1   0    q2
q2   0    q3
q3   0    q3

Here, q3 is the only accepting state and q0 is the initial state. This assumes the input alphabet consists only of 0; if it consists of more than that, you will need a dead state and extra productions.

Translating from a DFA to a TM is left as an exercise.