I am looking for some examples of unary languages lay between $L$ and $NP$, i.e., $ L \subseteq NL \subseteq P = AL \subseteq NP $.
What I found after some search(e.g., Complexity zoo for unary languages):
- It is not known whether there is a NP-Complete unary language.
- There are many known results for automata models and sub-logarithmic space.
- There seems no Zoo-style reference yet.
For example, is there any unary language in $ NL $ but not known in $ L $, in $ P $ but not known in $ NL $ or log-space alternating hierarchy?
Or, what are "the hardest" unary languages in $ NP $?