The ARNN model relativises P = NP and P ≠ NP

In this paper we prove that the relations P = NP and P not equal NP relativise to the deterministic/non-deterministic artificial recurrent neural net (ARNN) with real weights (informally considered as oracles in Martin Davis (2006) [10,11 1]). 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 makes the ARNN an interesting but restricted model of computation. (C) 2013 Elsevier B.V. All rights reserved.