- Ambos-Spies, K. and Fejer, P. Degrees of unsolvability. Unpublished, 2006.Google Scholar
- Andréka, H., Németi, I. and Németi, P. General relativistic hypercomputing and foundation of mathematics. Natural Computing 8, 3 (2009), 499--516. Google ScholarDigital Library
- Beggs, E., Costa, J.F. and Tucker, J.V. Limits to measurement in experiments governed by algorithms. Mathematical Structures in Computer Science 20, 6 (2010), 1019--1050. Google ScholarDigital Library
- Binder, I., Braverman, M. and Yampolsky, M. Filled Julia sets with empty interior are computable. Foundations of Computational Mathematics 7, 4 (2007), 405--416. Google ScholarDigital Library
- Brooks, R. The relationship between matter and life. Nature 409 (2001), 409--411.Google ScholarCross Ref
- Brooks, R. The case for embodied intelligence. In Alan Turing---His Work and Impact. S.B. Cooper and J. van Leeuwen, Eds. Elsevier Science, to appear.Google Scholar
- Calude, C.S. and Svozil, K. Quantum randomness and value indefiniteness. Advanced Science Letters 1 (2008), 165--168.Google ScholarCross Ref
- Chaitin, G.J. Metaphysics, metamathematics and metabiology. In Randomness Through Computation: Some Answers, More Questions. H. Zenil, Ed. World Scientific, Singapore, 2011.Google ScholarCross Ref
- Cooper, S.B. Emergence as a computability-theoretic phenomenon. Applied Mathematics and Computation 215, 4 (2009), 1351--1360.Google ScholarDigital Library
- Cooper, S.B. and Odifreddi, P. Incomputability in nature. In Computability and Models: Perspectives East and West. S.B. Cooper and S.S. Goncharov, Eds. Plenum, New York, 2003, 137--160.Google ScholarCross Ref
- Copeland, B.J. Even Turing machines can compute uncomputable functions. In Unconventional Models of Computation. C. Calude, J. Casti, and M. Dinneen, Eds. Springer-Verlag, 1998, 150--164.Google Scholar
- Costa, J.F., Loff, B. and Mycka, J. A foundations for real recursive function theory. Annals of Pure and Applied Logic 160, 3 (2009), 255--288.Google ScholarCross Ref
- Davis, M. The myth of hypercomputation. In Alan Turing: Life and Legacy of a Great Thinker. C. Teuscher, Ed. Springer-Verlag, 2004.Google Scholar
- Davis, M. Why there is no such discipline as hypercomputation. Applied Mathematics and Computation 178 (2006), 4--7.Google ScholarCross Ref
- Deutsch, D. Quantum theory, the Church-Turing principle, and the universal quantum computer. In Proceedings of the Royal Society A400 (1985) 97--117.Google ScholarCross Ref
- Hertling, P. Is the Mandelbrot set computable? Math. Logic Quarterly 51 (2005), 5--18.Google ScholarCross Ref
- Hodges, A. Alan Turing: The Enigma. Arrow, 1992. Google ScholarDigital Library
- Kreisel, G. Church's thesis: A kind of reducibility axiom for constructive mathematics. In Intuitionism and Proof Theory. A. Kino, J. Myhill, and R. E. Vesley, Eds. North-Holland, 1970, 121--150.Google Scholar
- Leavitt, D. The Man Who Knew Too Much: Alan Turing and the Invention of the Computer. W. W. Norton, 2006. Google ScholarDigital Library
- Matiyasevich, Y. Hilbert's Tenth Problem. MIT Press, Cambridge, 1993. Google ScholarDigital Library
- Murray, J.D. Mathematical Biology: I. An Introduction. 3rd Edition. Springer, NY, 2002.Google ScholarCross Ref
- Myhill, J. Creative sets. Z. Math. Logik Grundlagen Math. 1 (1955), 97--108.Google ScholarCross Ref
- Németi, I. and Dávid, G. Relativistic computers and the Turing barrier. Journal of Applied Mathematics and Computation 178 (2006), 118--142.Google ScholarCross Ref
- Odifreddi, P. Little steps for little feet; http://cs.nyu.edu/pipermail/fom/1999-august/003292.html.Google Scholar
- Pinker, S. How the Mind Works. W.W. Norton, New York, 1997.Google Scholar
- Pour-El, M.B. and Zhong, N. The wave equation with computable initial data whose unique solution is nowhere computable. Math. Logic Quarterly 43 (1997), 449--509.Google ScholarCross Ref
- Prigogine, I. From Being To Becoming. W.H. Freeman, New York, 1980.Google Scholar
- Prigogine, I. The End of Certainty: Time, Chaos and the New Laws of Nature. Free Press, New York, 1997.Google Scholar
- Rozenberg, G., Bäck, T.B. and Kok, J.N., Eds. Handbook of Natural Computing. Springer, 2011. Google ScholarDigital Library
- Saari, D.G. and Xia, Z.J. Off to infinity in finite time. Notices of the American Mathematical Society 42, 5 (1995), 538--546.Google Scholar
- Sloman, A. Some requirements for human-like robots: Why the recent over-emphasis on embodiment has held up progress. In Creating Brain-Like Intelligence LNCS 5436. B. Sendhoff et al., Eds. Springer, 2009, 248--277. Google ScholarDigital Library
- Smolensky, P. On the proper treatment of connectionism. Behavioral and Brain Sciences 11, 1 (1988), 1--74.Google ScholarCross Ref
- Teuscher, C. Turing's Connectionism. An Investigation of Neural Network Architectures. Springer-Verlag, London, 2002. Google ScholarDigital Library
- Turing, A.M. On computable numbers with an application to the Entscheidungs problem. In Proceedings London Mathematical Society 42 (1936), 230--265.Google Scholar
- Turing, A.M. The chemical basis of morphogenesis. Phil. Trans. of the Royal Society of London. Series B, Biological Sciences 237, 641 (1952), 37--72.Google Scholar
- Velupillai, K.V. Uncomputability and undecidability in economic theory. Applied Mathematics and Computation 215, 4 (Oct. 2009), 1404--1416.Google Scholar
- Wegner, P. and Goldin, D. The Church-Turing Thesis: Breaking the myth. In CiE: New Computational Paradigms LNCS 3526. S.B. Cooper and B. Löwe, Eds. Springer, 2005. Google ScholarDigital Library
- Wiedermann, J. and van Leeuwen, J. How we think of computing today. Logic and Theory of algorithms LNCS 5028. A. Beckmann, C. Dimitracopoulos, and B. Löwe, Eds. Springer-Verlag, Berlin, 2008, 579--593. Google ScholarDigital Library
- Yates, C.E.M. On the degrees of index sets. Transactions of the American Mathematical Society 121 (1966), 309--328.Google ScholarCross Ref
- Ziegler, M. Physically-relativized Church-Turing Hypotheses. Applied Mathematics and Computation 215, 4 (2009), 1431--1447.Google ScholarDigital Library
Index Terms
- Turing's Titanic machine?
Recommendations
Understanding the Universal Turing Machine: an implementation in JFLAP
We describe the implementation of a Universal Turing Machine for the JFLAP platform. JFLAP is most successful and widely used tool for visualizing and simulating automata such as finite state machines, pushdown automata, and Turing Machines. By ...
Some properties of one-pebble turing machines with sublogarithmic space
This paper investigates some aspects of the accepting powers of deterministic, nondeterministic, and alternating one-pebble Turing machines with spaces between log log n and log n. We first investigate a relationship between the accepting powers of two-...
What Turing Did after He Invented the Universal Turing Machine
Alan Turing anticipated many areas of current research in computer and cognitive science. This article outlines his contributions to Artificial Intelligence, connectionism, hypercomputation, and Artificial Life, and also describes Turing's pioneering role ...
Comments