Robust Simulations of Turing Machines with Analytic Maps and Flows

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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.

Our interest in the questions addressed in this paper was raised by past discussions with Félix Costa and Cris Moore. This work was partially supported by Fundaçã o para a Ciência e a Tecnologia (FCT) and FEDER via the Center for Logic and Computation – CLC, the project ConTComp POCTI/MAT/45978/2002 and grant SFRH/BD/17436/2004. Additional support was also provided by the Fundaçã o Calouste Gulbenkian through the Programa Gulbenkian de Estímulo à Investigaçã o.