Abstract
One of the main current issues about hypercomputation concerns the claim of the possibility of building a physical device that hypercomputes. In order to prove this claim, one possible strategy could be to physically build an oracle hypermachine, namely a device which is be able to use some extern information from nature to go beyond Turing machines limits. However, there is an epistemological problem affecting this strategy, which may be called “verification problem”. This problem raises in presence of an oracle hypermachine and it may be set out as follows: even if we were able to build such a hypermachine we would not be able to claim that it hypercomputes because it would be impossible to verify that the machine can compute a non Turing-computable function. In this paper, I propose an analysis of the verification problem in order to know whether it is a genuine problem for oracle hypermachines.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Adleman, L.M., Blum, M.: Inductive Inference and Unsolvability. The Journal of Symbolic Logic 56, 891–900 (1991)
Calude, C.S.: Algorithmic randomness, quantum physics, and incompleteness. In: Margenstern, M. (ed.) MCU 2004. LNCS, vol. 3354, pp. 1–17. Springer, Heidelberg (2005)
Calude, C.S., Svozil, K.: Quantum Randomness and Value Indefiniteness. Advanced Science Letters 1, 165–168 (2008)
Chaitin, G.: On the Length of Programs for Computing Finite Binary Sequences. Journal of the Association for Computing Machinery 13, 547–569 (1966)
Church, A.: On the Concept of a Random Sequence. Bulletin of the American Mathematical Society 46, 130–135 (1940)
Cleland, C.E.: The Concept of Computability. Theoretical Computer Science 317, 209–225 (2004)
Copeland, J.: Narrow Versus Wide Mechanism: Including a Re-Examination of Turing’s Views of the Mind-Machine Issue. The Journal of Philosophy 1, 5–32 (2000)
Copeland, J.: Hypercomputation. Minds and Machines 12, 461–502 (2002)
Copeland, J.: Accelerating Turing Machine. Minds and Machines 12, 281–301 (2002)
Copeland, J., Proudfoot, D.: Alan Turing’s Forgotten Ideas in Computer Science. Scientific American 208, 76–81 (1999)
Davies, B.: Building Infinite Machines. British Journal for the Philosophy of Science 52, 671–682 (2001)
Davis, M.: The Myth of Hypercomputation. In: Teuscher, C. (ed.) Alan Turing: The Life and Legacy of a Great Thinker, pp. 195–212. Springer, Berlin (2004)
De Leeuw, K., Moore, E.F., Shannon, C.E., Shapiro, N.: Computability by Probabilistic Machines. Automata Studies. Princeton University Press (1956)
Earman, J.: Bangs, Crunchs, Whimpers and Shrieks - Singularities and Acausalities in Relativistic Spacetimes. Oxford University Press, Oxford (1995)
Gold, M.: Limiting Recursion. The Journal of Symbolic Logic 30, 28–48 (1965)
Hamkins, J.D.: Infinite Time Turing Machines. Minds and Machines 12, 567–604 (2002)
Hogarth, M.: Does General Relativity Allow an Observer to View an Eternity in a Finite Time? Foundations of Physics Letters 5, 173–181 (1992)
Jennewein, T., Achleitner, U., Weihs, G., Weinfurter, H., Zeilinger, A.: A Fast and Compact Quantum Random Number Generator. Review of Scientific Instruments 71, 1675–1680 (2000)
Kieu, T.: Quantum Hypercomputation. Minds and Machines 12, 541–561 (2002)
Leitsch, A., Schachner, G., Svozil, K.: How to Acknowledge Hypercomputation? Complex Systems 18, 131–143 (2008)
Loff, B., Costa, J.F.: Five Views of Hypercomputation. International Journal of Unconventional Computing 5, 193–207 (2009)
Martin-Löf, P.: The Definition of a Random Sequence. Information and Control 9, 602–619 (1966)
Matiiassevitch, Y.: Le Dixième Problème de Hilbert: son Indécidabilité. Masson, Paris (1995)
Piccinini, G.: The Physical Church-Turing Thesis: Modest or Bold? The British Journal For The Philosophy of Science 62, 773–769 (2011)
Pitowski, I.: The Pysical Church Thesis and Physical Computational Complexity. Iyyun 39, 81–99 (1990)
Shagrir, O., Pitowski, I.: Physical Hypercomputation and the Church-Turing Thesis. Minds and Machines 13, 87–101 (2003)
Siegelmann, H.T.: Neural and Super-Turing Computing. Minds and Machines 13, 103–114 (2003)
Stannett, M.: Computation and Hypercomputation. Minds and Machines 13, 115–153 (2003)
Stannett, M.: Hypercomputational Models. In: Teuscher, C. (ed.) Alan Turing: The Life and Legacy of a Great Thinker, pp. 135–157. Springer, Berlin (2004)
Turing, A.M.: Systems of Logic Based on the Ordinals. In: Davis, M. (ed.) The Undecidable, pp. 154–222. Dover, New York (1939, 1965)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Franchette, F. (2013). Oracle Hypermachines Faced with the Verification Problem. In: Dodig-Crnkovic, G., Giovagnoli, R. (eds) Computing Nature. Studies in Applied Philosophy, Epistemology and Rational Ethics, vol 7. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-37225-4_13
Download citation
DOI: https://doi.org/10.1007/978-3-642-37225-4_13
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-37224-7
Online ISBN: 978-3-642-37225-4
eBook Packages: EngineeringEngineering (R0)