On the P-NP problem over real matrix rings

Authors:
A. Rybalov
Affiliations:
Department of Mathematical Logic, Omsk State University, prospekt Mira 55a, Omsk 644077, Russia
Venue:
Theoretical Computer Science
Year:
2004

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Abstract

We prove that P ≠ DNP over rings of matrices with real elements in a restricted Blum-Shub-Smale computational model. The restriction is that machines can use only two constants (zero-matrix and identity matrix) in computations. Also we show that in the unrestricted Blum-Shub-Smale model P = DNP over real matrix rings iff P = DNP over the non-ordered real ring and the same is true for the equality P = NP. The latter assertion implies that P ≠ NP over real matrix rings.