can it be said that NL^NL = NL?
It's not quite as simple. Calls to oracle have a &quot;magic&quot; quality of taking only one unit of time. Even if NL can simulate the oracle calls, these simulated invocations of the oracle can take more resources than is needed by the oracle machine. To prove these classes equal you need to prove that calls to the oracle do not improve performance in the computational complexity sense because producing the input to the oracle already requires sufficient resources that the oracle machine cannot use this &quot;magic&quot; to get improved performance.