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Computable Scientists, Uncomputable World

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6079))

Abstract

Consider the classical model of a Turing machine with an oracle. The classical oracle is a one step external consultation device. The oracle may contain either non-computable information, or computable information provided just to speed up the computations of the Turing machine.

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References

  1. Beggs, E., Costa, J.F., Loff, B., Tucker, J.V.: Computational complexity with experiments as oracles. Proceedings of the Royal Society, Series A (Mathematical, Physical and Engineering Sciences) 464(2098), 2777–2801 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  2. Beggs, E., Costa, J.F., Loff, B., Tucker, J.V.: Computational complexity with experiments as oracles II. Upper bounds. Proceedings of the Royal Society, Series A (Mathematical, Physical and Engineering Sciences) 465(2105), 1453–1465 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  3. Beggs, E., Costa, J.F., Tucker, J.: Physical oracles: the Turing machine and the Wheatstone bridge. In: Studia Logica, Trends in Logic VI: The Contributions of Logic to the Foundations of Physics, 22 p. (to appear 2010)

    Google Scholar 

  4. Beggs, E., Costa, J.F., Tucker, J.V.: Computational Models of Measurement and Hempel’s Axiomatization. In: Carsetti, A. (ed.) Causality, Meaningful Complexity and Knowledge Construction. Theory and Decision Library A, vol. 46, pp. 155–184. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  5. Beggs, E., Costa, J.F., Tucker, J.V.: Physical experiments as oracles. Bulletin of the European Association for Theoretical Computer Science 97, 137–151 (2009); An invited paper for the Natural Computing Column

    MathSciNet  Google Scholar 

  6. Beggs, E., Costa, J.F., Tucker, J.V.: Limits to measurement in experiments governed by algorithms, 33 p. (submitted 2010)

    Google Scholar 

  7. Bohm, D.: Wholeness and the Implicate Order. Routledge, New York (1996)

    Google Scholar 

  8. Bournez, O., Cosnard, M.: On the computational power of dynamical systems and hybrid systems. Theoretical Computer Science 168(2), 417–459 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  9. Campbell, N.R.: Foundations of Science, The Philosophy of Theory and Experiment. Dover, New York (1957)

    Google Scholar 

  10. Carnap, R.: Philosophical Foundations of Physics. Basic Books, New York (1966)

    Google Scholar 

  11. Geroch, R., Hartle, J.B.: Computability and Physical Theories. Foundations of Physics 16(6), 533–550 (1986)

    Article  MathSciNet  Google Scholar 

  12. Hempel, C.G.: Fundamentals of concept formation in empirical science. International Encyclopedia of Unified Science 2(7) (1952)

    Google Scholar 

  13. Jain, S., Osherson, D., Royer, J.S., Sharma, A.: Systems That Learn. In: An Introduction to Learning Theory. The MIT Press, Cambridge (1999)

    Google Scholar 

  14. Krantz, D.H., Suppes, P., Luce, R.D., Tversky, A.: Foundations of Measurement. Dover, New York (2009)

    Google Scholar 

  15. Siegelmann, H.T.: Neural Networks and Analog Computation: Beyond the Turing Limit. Birkhäuser, Basel (1999)

    MATH  Google Scholar 

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Costa, J.F. (2010). Computable Scientists, Uncomputable World. In: Calude, C.S., Hagiya, M., Morita, K., Rozenberg, G., Timmis, J. (eds) Unconventional Computation. UC 2010. Lecture Notes in Computer Science, vol 6079. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13523-1_4

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  • DOI: https://doi.org/10.1007/978-3-642-13523-1_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-13522-4

  • Online ISBN: 978-3-642-13523-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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