Implementing turing machines in dynamic field architectures

AISB/IACAP World Congress 2012 - 5th AISB Symposium on Computing and Philosophy: Computing, Philosophy and the Question of Bio-Machine Hybrids, Part of Alan Turing Year 2012

Volumn , Issue , 2012, Pages 36-40

  Graben, Peter Beim ^a   Potthast, Roland ^b  

^a HUMBOLDT UNIVERSITY   (Germany)

^b UNIVERSITY OF READING   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

DYNAMIC FIELD THEORIES; INTEGRAL TRANSFORMATIONS; MACHINE COMPUTATIONS; NEURAL FIELD EQUATIONS; RANDOM INITIAL CONDITIONS; RANDOMLY DISTRIBUTED; RECTANGULAR PARTITION; SYMBOLIC INTERPRETATION;

INTEGRAL EQUATIONS; MACHINERY; NONLINEAR DYNAMICAL SYSTEMS; ONTOLOGY; PHASE SPACE METHODS; PROBABILITY DISTRIBUTIONS; TURING MACHINES;

DYNAMICS;

EID: 84893186599     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (34)

1. S.-I. Amari, Dynamics of pattern formation in lateral-inhibition type neural fields, Biological Cybernetics, 27, 77-87, (1977).
2. J. R. Anderson, Cognitive Psychology and its Implications,W. H. Freeman and Company, New York (NY), 1995.
3. H. Atmanspacher and P. beim Graben, Contextual emergence of mental states from neurodynamics, Chaos and Complexity Letters, 2(2/3), 151-168, (2007).
4. H. Atmanspacher and P. beim Graben, Contextual emergence, Scholarpedia, 4(3), 7997, (2009).
5. R. C. Bishop and H. Atmanspacher, Contextual emergence in the description of properties, Foundations of Physics, 36(12), 1753-1777, (2006).
6. P. Cvitanović, G. H. Gunaratne, and I. Procaccia, Topological and metric properties of Hénon-type strange attractors, Physical Reviews A, 38(3), 1503-1520, (1988).
7. W. Erlhagen and G. Schöner, Dynamic field theory of movement preparation, Psychological Review, 109(3), 545-572, (2002).
8. J. Fodor and Z. W. Pylyshyn, Connectionism and cognitive architecture: A critical analysis, Cognition, 28, 3-71, (1988).
9. P. beim Graben, Incompatible implementations of physical symbol systems, Mind and Matter, 2(2), 29-51, (2004).
10. P. beim Graben, S. Gerth, and S. Vasishth, Towards dynamical system models of language-related brain potentials, Cognitive Neurodynamics, 2(3), 229-255, (2008).
11. P. beim Graben, B. Jurish, D. Saddy, and S. Frisch, Language processing by dynamical systems, International Journal of Bifurcation and Chaos, 14(2), 599-621, (2004).
12. P. beim Graben and R. Potthast, Inverse problems in dynamic cognitive modeling, Chaos, 19(1), 015103, (2009).
13. J. E. Hopcroft and J. D. Ullman, Introduction to Automata Theory, Languages, and Computation, Addison-Wesley, Menlo Park, California, 1979.
14. M. B. Kennel and M. Buhl, Estimating good discrete partitions from observed data: Symbolic false nearest neighbors, Physical Review Letters, 91(8), 084102, (2003).
15. B. O. Koopman, Hamiltonian systems and transformations in Hilbert space, Proceedings of the National Academy of Sciences of the U.S.A., 17, 315-318, (1931).
16. B. O. Koopman and J. von Neumann, Dynamical systems of continuous spectra, Proceedings of the National Academy of Sciences of the U.S.A., 18, 255-262, (1932).
17. D. Lind and B. Marcus, An Introduction to Symbolic Dynamics and Coding, Cambridge University Press, Cambridge (UK), 1995.
18. B. McMillan, The basic theorems of information theory, 24, 196-219, (1953).
19. C. Moore, Unpredictability and undecidability in dynamical systems, Physical Review Letters, 64(20), 2354-2357, (1990).
20. C. Moore, Generalized shifts: unpredictability and undecidability in dynamical systems, Nonlinearity, 4, 199-230, (1991).
21. C. Moore, Dynamical recognizers: real-time language recognition by analog computers, Theoretical Computer Science, 201, 99-136, (1998).
22. E. Ott, Chaos in Dynamical Systems, Cambridge University Press, New York, 1993.
23. J. B. Pollack, The induction of dynamical recognizers, Machine Learning, 7, 227-252, (1991). Also published in [24], pp. 283-312.
24. Mind as Motion: Explorations in the Dynamics of Cognition, eds., R. F. Port and T. van Gelder, MIT Press, Cambridge (MA), 1995.
25. R. Potthast and P. beim Graben, Inverse problems in neural field theory, SIAM Jounal on Applied Dynamical Systems, 8(4), 1405-1433, (2009).
26. G. Schöner and E. Dineva, Dynamic instabilities as mechanisms for emergence, Developmental Science, 10(1), 69-74, (2007).
27. H. T. Siegelmann, Computation beyond the Turing limit, Science, 268(5210), 545-548, (1995).
28. H. T. Siegelmann, The simple dynamics of super Turing theories, Theoretical Computer Science, 168, 461-472, (1996).
29. H. T. Siegelmann and E. D. Sontag, On the computational power of neural nets, Journal of Computer and System Sciences, 50(1), 132-150, (1995).
30. P. Smolensky, On the proper treatment of connectionism, Behavioral and Brain Sciences, 11(1), 1-74, (1988).
31. W. Tabor, Fractal encoding of context-free grammars in connectionist networks, Expert Systems: The International Journal of Knowledge Engineering and Neural Networks, 17(1), 41-56, (2000).
32. W. Tabor, A dynamical systems perspective on the relationship between symbolic and non-symbolic computation, Cognitive Neurodynamics, 3(4), 415-427, (2009).
33. A. M. Turing, On computable numbers, with an application to the Entscheidungsproblem, Proceedings of the London Mathematical Society, 2(42), 230-265, (1937).
34. H. R.Wilson and J. D. Cowan, A mathematical theory of the functional dynamics of cortical and thalamic nervous tissue, Kybernetik, 13, 55-80, (1973).