Abstract
Reaction–diffusion models are commonly used to describe dynamical processes in complex physical, chemical and biological systems. Applications of these models range from pattern formation or epidemic spreads to natural selection through ecological systems and percolation systems. Reaction refers to phenomena where two or more entities become in contact and modify their state as a consequence of this fact. Diffusion implies the existence of a space where the involved entities are situated and can move. The Reaction–Diffusion Machine is a computational model we previously introduced inspired by reaction diffusion phenomena. In this work, we prove that a Deterministic Turing Machine can be simulated by a Reaction-Diffusion Machine.
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References
Turing, A.: The chemical basis of morphogenesis. Philos. Trans. R. Society 237 (1952)
Cantrell, R.S., Cosner, C.: Spatial Ecology via Reaction–Diffusion Equations. Wiley, Chichester (2003)
Bandini, S., Mauri, G., Pavesi, G., Simone, C.: A parallel model based on Cellular Automata for the simulation of pesticide percolation in the soil. In: Malyshkin, V.E. (ed.) PaCT 1999. LNCS, vol. 1662, pp. 383–394. Springer, Heidelberg (1999)
Simone, C., Bandini, S.: The reaction–diffusion methaphor for modeling cooperative work. Prestige J. of Management and Research 2(1), 1–21 (1998)
Bandini, S., Simone, C.: Integrating forms of interaction in a distributed model. Fundamenta Informaticae 61(1), 1–17 (2004)
Garey, M.R., Johnson, D.S.: Computers and Intractability. A Guide to the Theory of NP–Completeness. Freeman and Company, San Francisco (1979)
Boudol, G., Berry, G.: The chemical abstract machine. Theoretical Computer Science 96(1) (1992)
Simone, C., Bandini, S.: Integrating awareness in cooperative applications through the reaction–diffusion metaphor. Computer Supported Cooperative Work 11(3-4), 495–530 (2002)
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© 2005 Springer-Verlag Berlin Heidelberg
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Bandini, S., Mauri, G., Pavesi, G., Simone, C. (2005). Computing with a Distributed Reaction-Diffusion Model. In: Margenstern, M. (eds) Machines, Computations, and Universality. MCU 2004. Lecture Notes in Computer Science, vol 3354. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-31834-7_7
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DOI: https://doi.org/10.1007/978-3-540-31834-7_7
Publisher Name: Springer, Berlin, Heidelberg
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