The ARNN model relativises P =NP and P≠NP

Authors:
José Félix Costa;Raimundo Leong
Affiliations:
Department of Mathematics, Instituto Superior Técnico, Technical University of Lisbon, Lisbon, Portugal and Centro de Matemática e Aplicaçíes Fundamentais do Complexo Interdisc ...;Department of Mathematics, Instituto Superior Técnico, Technical University of Lisbon, Lisbon, Portugal
Venue:
Theoretical Computer Science
Year:
2013

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Abstract

In this paper we prove that the relations P=NP and PNP relativise to the deterministic/non-deterministic artificial recurrent neural net (ARNN) with real weights (informally considered as oracles in Martin Davis (2006) [10,11]). 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.