The P ≠ NP conjecture in the context of real and complex analysis

Authors:
Jerzy Mycka;José Félix Costa
Affiliations:
Institute of Mathematics, University of Maria Curie-Sklodowska, Lublin, Poland;Department of Mathematics, I.S.T., Universidade Técnica de Lisboa, Lisboa, Portugal
Venue:
Journal of Complexity
Year:
2006

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Abstract

In this paper, we aim at an analog characterization of the classical P ≠ NP conjecture of Structural Complexity. We consider functions over continuous real and complex valued variables. Subclasses of functions can be defined using Laplace transforms adapted to continuous-time computation, introducing analog classes DAnalog and NAnalog. We then show that if DAnalog ≠ NAnalog then P ≠ NP.