Chapter

New Computational Paradigms

Volume 3526 of the series Lecture Notes in Computer Science pp 169-179

Robust Simulations of Turing Machines with Analytic Maps and Flows

  • Daniel S. GraçaAffiliated withDepartamento de Matemática, Faculdade de Ciências e Tecnologia, Universidade do AlgarveCenter for Logic and Computation, Departamento de Matemática, Instituto Superior Técnico, Universidade Técnica de Lisboa
  • , Manuel L. CampagnoloAffiliated withCenter for Logic and Computation, Departamento de Matemática, Instituto Superior Técnico, Universidade Técnica de LisboaDepartamento de Matemática, Instituto Superior de Agronomia, Universidade Técnica de Lisboa
  • , Jorge BuescuAffiliated withCenter for Mathematical Analysis, Geometry and Dynamical Systems, Departamento de Matemática, Instituto Superior Técnico, Universidade Técnica de Lisboa

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Abstract

In this paper, we show that closed-form analytic maps and flows can simulate Turing machines in an error-robust manner. The maps and ODEs defining the flows are explicitly obtained and the simulation is performed in real time.