The ARNN model relativises P=NP and P!=NP

In this paper we prove that the relations P = NP and P 6= NP relativise to the deterministic / non-deterministic artificial recurrent neural net (ARNN ) with real weights (informally considered as oracles in [1] and [2]). Although, in the nineties, a dozen of papers were written on the ARNN model, some introducing computation via neural nets with real weights and some introducing non-deterministic and stochastic neural nets, it seems that no one noticed such a relativisation, which is also true of many other non-standard models of computation involving real-valued parameters.