We study the complexity relationship between three models of unbounded memory
automata: nu-automata (ν-A), Layered Memory Automata (LaMA)and
History-Register Automata (HRA). These are all extensions of finite state
automata with unbounded memory over infinite alphabets. We prove that the
membership problem is NP-complete for all of them, while they fall into
different classes for what concerns non-emptiness. The problem of non-emptiness
is known to be Ackermann-complete for HRA, we prove that it is PSPACE-complete
for ν-A