Abstract
We advance a Bayesian concept of intrinsic asymptotic universality, taking to its final conclusions previous conceptual and numerical work based upon a concept of a reprogrammability test and an investigation of the complex qualitative behaviour of computer programs. Our method may quantify the trust and confidence of the computing capabilities of natural and classical systems, and quantify computers by their degree of reprogrammability. We test the method to provide evidence in favour of a conjecture concerning the computing capabilities of Busy Beaver Turing machines as candidates for Turing universality. The method has recently been used to quantify the number of intrinsically universal cellular automata , with results that point towards the pervasiveness of universality due to a widespread capacity for emulation. Our method represents an unconventional approach to the classical and seminal concept of Turing universality, and it may be extended and applied in a broader context to natural computation, by (in something like the spirit of the Turing test) observing the behaviour of a system under circumstances where formal proofs of universality are difficult, if not impossible to come by.
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
References
Bennett, C.H.: Logical depth and physical complexity. The Universal Turing Machine A Half-Century Survey, pp. 207–235. Springer, Heidelberg (1995)
Calude, C.S., Stay, M.A.: Most programs stop quickly or never halt. Adv. Appl. Math. 40(3), 295–308 (2008)
Chaitin, G.J.: Computing the Busy Beaver Function. Open Problems in Communication and Computation, pp. 108–112. Springer, New York (1987)
Delahaye, J.-P., Zenil, H.: Numerical Evaluation of the Complexity of Short Strings: a Glance Into the Innermost Structure of Algorithmic Randomness. Appl. Math. Comput. 219, 63–77 (2012)
Durand, B., Zsuzsanna R.: The game of life: universality revisited. Cellular Automata, pp. 51–74. Springer, Heidelberg (1999)
von Neumann J.: Theory of Self-reproducing Automata, Burks A.W. (ed.), University of Illinois Press, Urbana, Ill., (1966)
Păun, G.: Introduction to Membrane Computing. Applications of Membrane Computing. pp. 1–42. Springer, Berlin (2006)
Riedel J., Zenil H.: Cross-boundary Behavioural Reprogrammability Reveals Evidence of Pervasive Turing Universality, (ArXiv preprint). arXiv:1510.01671
Ollinger N.: The quest for small universal cellular automata. In: Widmayer P., Triguero F., Morales R, Hennessy M., Eidenbenz S. and Conejo R. (eds.) Proceedings of International Colloquium on Automata, languages and programming (ICALP’2002), LNCS, vol. 2380, pp. 318–329, (2002)
Ollinger N., The intrinsic universality problem of one-dimensional cellular automata, Symposium on Theoretical Aspects of Computer Science (STACS’2003), Alt H. and Habib M. (eds.), LNCS 2607, pp. 632–641, 2003
Rado, T.: On Noncomputable Functions. Bell Syst. Tech. J. 41(3), 877–884 (1962)
Terrazas, G., Zenil, H., Krasnogor, N.: Exploring Programmable Self-Assembly in Non DNA-based Computing. Nat. Comput. 12(4), 499–515 (2013)
Wolfram, S.: Table of Cellular Automaton Properties. Theory and Applications of Cellular Automata, pp. 485–557. World Scientific, Singapore (1986)
Wolfram, S.: Statistical mechanics of cellular automata. Rev. Mod. Phys. 55, 601–644 (1983)
Wolfram, S.: A New Kind of Science. Wolfram Science. Il, Chicago (2002)
Zenil, H., Beaver, B.: Wolfram Demonstrations Project. http://demonstrations.wolfram.com/BusyBeaver/
Zenil, H., Villarreal-Zapata, E.: Asymptotic behaviour and ratios of complexity in cellular automata rule spaces. Int. J. Bifurc. Chaos, 13(9) (2013)
Zenil, H.: On the Dynamic Qualitative Behaviour of Universal Computation. Complex Systems 20(3), 265–277 (2012)
Zenil, H.: Algorithmicity and programmability in natural computing with the game of life as an In silico case study. J. Exp. Theor. Artif. Intell. 27(1), 109–121 (2015)
Zenil, H.: A behavioural foundation for natural computing and a programmability test. In: Dodig-Crnkovic, G., Giovagnoli, R. (eds.) Computing Nature: Turing Centenary Perspective, SAPERE Series, vol. 7, pp. 87–113. Springer, Heidelberg (2013)
Zenil, H.: What is nature-like computation? A behavioural approach and a notion of programmability. Philos. Tech. 27(3), 399–421 (2014) (online: 2012)
Zenil, H.: From computer runtimes to the length of proofs: With an algorithmic probabilistic application to waiting times in automatic theorem proving. In: Dinneen, M.J., Khousainov, B., Nies, A. (eds.) Computation, Physics and Beyond International Workshop on Theoretical Computer Science, WTCS 2012, LNCS, vol. 7160, pp. 223–240. Springer, Heidelberg (2012)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Zenil, H., Riedel, J. (2017). Asymptotic Intrinsic Universality and Natural Reprogrammability by Behavioural Emulation. In: Adamatzky, A. (eds) Advances in Unconventional Computing. Emergence, Complexity and Computation, vol 22. Springer, Cham. https://doi.org/10.1007/978-3-319-33924-5_9
Download citation
DOI: https://doi.org/10.1007/978-3-319-33924-5_9
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-33923-8
Online ISBN: 978-3-319-33924-5
eBook Packages: EngineeringEngineering (R0)