$L = (0^i 1)^n$ where i=1,2,3,4...n and n>=0
For eg :- 00010001 doesn't belong to the language as n=2 but i=3 at the beginning.
001001001 belongs to L as n=3 and i=2 in all cases.
I know the above language is not regular for sure as value of 'i' depends on value of 'n' and it requires comparison. So DFA not possible.
Now I am not sure to which class of language does the above language belong because to check number of zeroes or 'i', we need value of 'n' which can be found out only after reading the entire string.
Can someone please help?