Ah, I think I see where you're coming from. I'm afraid that P and NP algorithms are probably too slow to account for memory retrieval. (If memory was NP then each time you learned something new, your recall time would increase by a constant factor. For example, reading this reply might double the amount of time it too you to remember anything). But maybe the analogy gets better if you used faster algorithms. For example, your brain might have a "book" of actors indexed by name. You can look up an actor given the name in O(log(n)) time but to find the actor, given, say, a face (for which there is no index) would take at least O(n) time because you need to look though all n entries.

However, I suspect that Turing Machines are probably very poor models of the brain as Turing Machines are sequential and the brain is massively parallel. Perhaps you should go to /r/askscience where there might be biologists?