Abstract
By experimental computation we mean the idea of computing a function by experimenting with some physical equipment. To analyse the functions computable by experiment, we are developing a methodology that chooses a precise specification of a physical theory T and derives precise descriptions of the procedures and equipment the theory allows. As a case study, we choose a fragment T of Newtonian kinematics and describe a language EP(T), and some of its extensions, for expressing experimental procedures allowed by T. The languages for experimental procedures are similar to imperative programming languages that express algorithmic procedures. We show that EP(T) can define all functions on the rational numbers that are definable by algorithms.
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References
Akl, S.G.: Conventional or unconventional: Is any computer universal? In: Adamatzky, A., Teuscher, C. (eds.) From Utopian to Genuine Unconventional Computers, pp. 101–136. Luniver Press, Frome (2006)
Beggs, E. J., Tucker, J.V.: Computations via experiments with kinematic systems, Research Report 4.04, Department of Mathematics, University of Wales Swansea, March 2004 or Technical Report 5-2004, Department of Computer Science, University of Wales Swansea (March 2004)
Beggs, E.J., Tucker, J. V.: Embedding infinitely parallel computation in Newtonian kinematics. Applied Mathematics and Computation 178, 25–43 (2006)
Beggs, E. J., Tucker, J.V.: Can Newtonian systems, bounded in space, time, mass and energy compute all functions? Theoretical Computer Science 371, 4–19 (2007)
Beggs, E.J., Tucker, J. V.: Experimental computation of real numbers by Newtonian machines. Proceedings Royal Society Series A 463, 1541–1561 (2007)
Beggs, E.J., Costa, J.F., Loff, B., Tucker, J.V.: Computational complexity with experiments as oracles (in preparation, 2008)
Chen, F., Rosu, G., Venkatesan, R.P.: Rule-based analysis of dimensional safety. In: Nieuwenhuis, R. (ed.) RTA 2003. LNCS, vol. 2706. Springer, Heidelberg (2003)
Geroch, R., Hartle, J.B.: Computability and physical theories. Foundations of Physics 16, 533–550 (1986)
Griffor, E. (ed.): Handbook of Computability Theory. Elsevier, Amsterdam (1999)
Fredkin, E., Toffoli, T.: Conservative logic. International Journal of Theoretical Physics 21, 219–253 (1982)
Kreisel, G.: A notion of mechanistic theory. Synthese 29, 9–24 (1974)
Odifreddi, P.: Classical Recursion Theory. Studies in Logic and the Foundations of mathematics, vol. 129. North-Holland, Amsterdam (1989)
Pour-El, M.B., Richards, J.I.: Computability in Analysis and Physics, Perspectives in Mathematical Logic. Springer, Berlin (1989)
Stoltenberg-Hansen, V., Tucker, J.V.: Effective algebras. In: Abramsky, S., Gabbay, D., Maibaum, T. (eds.) Handbook of Logic in Computer Science. Semantic Modelling, vol. IV, pp. 357–526. Oxford University Press, Oxford (1995)
Stoltenberg-Hansen, V., Tucker, J.V.: Computable rings and fields. In: Griffor, E.R. (ed.) Handbook of Computability Theory, pp. 363–447. Elsevier, Amsterdam (1999)
Stoltenberg-Hansen, V., Tucker, J. V.: Concrete models of computation for topological algebras. Theoretical Computer Science 219, 347–378 (1999)
Stoltenberg-Hansen, V., Tucker, J. V.: Computable and continuous partial homomorphisms on metric partial algebras. Bulletin for Symbolic Logic 9, 299–334 (2003)
Tucker, J. V., Zucker, J.I.: Computable functions and semicomputable sets on many sorted algebras. In: Abramsky, S., Gabbay, D., Maibaum, T. (eds.) Handbook of Logic for Computer Science, vol. V, pp. 317–523. Oxford University Press, Oxford (2000)
Tucker, J. V., Zucker, J.I.: Abstract versus concrete computation on metric partial algebras. ACM Transactions on Computational Logic 5, 611–668 (2004)
Weihrauch, K.: Computable Analysis, An introduction. Springer, Heidelberg (2000)
Yao, A.: Classical physics and the Church Turing thesis. Journal ACM 50, 100–105 (2003)
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Beggs, E.J., Tucker, J.V. (2008). Programming Experimental Procedures for Newtonian Kinematic Machines. In: Beckmann, A., Dimitracopoulos, C., Löwe, B. (eds) Logic and Theory of Algorithms. CiE 2008. Lecture Notes in Computer Science, vol 5028. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-69407-6_6
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DOI: https://doi.org/10.1007/978-3-540-69407-6_6
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