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Optimizing Transition Order

  • Paul RendellEmail author
Chapter
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Part of the Emergence, Complexity and Computation book series (ECC, volume 18)

Abstract

The simple universal Turing machine designed to work with the Game of Life Turing machine contains a description of the target Turing machine in the form of a list of transitions. It will work with the transitions in any order. However the order makes is a great deal of difference to the size of the list on the universal Turing machine’s tape and the speed of operation. It was considered worth trying to minimise the size of the coded transition list for the unary multiplication Turing machine in order to minimize the size of the stacks required and therefore the size of the Game of Life pattern needed to run it. This optimisation is described in this chapter. It was found to be a quadratic assignment problem. A surprisingly simple procedure was found be successful in solving this simple example. The SUTM will work with the transitions in any order. However the order makes is a great deal of difference to the size of the list on the UTM tape and the speed of operation. It was considered worth trying to minimise the size of the coded transition list for the unary multiplication TM in order to minimize the size of the stacks required and therefore the size of the GoL pattern shown in Fig.  5.20.

References

  1. 1.
    Koopmans, T.C., Beckmann, M.: Assignment Problems and the Location of Economic Activities. Cowles Foundation Paper 108, reprinted from Econometric Journal of Econometric Society 25(1) (1957)Google Scholar
  2. 2.
    Loiola, E.M., Maria, N., Abreu, M., Boaventura-netto, P.O., Hahn, P., Querido, T.: An analytical survey for the quadratic assignment problem. Eur. J. Oper. Res. 657–690 (2007)Google Scholar
  3. 3.
    Rendell, P.: Java Applet Turing Machine Simulator. http://www.rendell-attic.org/gol/TMapplet (2009)
  4. 4.
    James, T., Rego, C., Glover, F.: Multistart Tabu search and diversification strategies for the quadratic assignment problem. IEEE Trans. Syst. Man Cybern. Part A: Syst. Hum. 39(3), 579–596 (2009)Google Scholar
  5. 5.
    Boese, K.D., Kahng, A.B., Muddu, S.: A new adaptive multi-start technique for combinatorial global optimizations. Oper. Res. Lett. 16, 101–113 (1994). Seminare Maurey-Schwartz (1975–1976)Google Scholar
  6. 6.
    Reeves, C.R.: Landscapes, operators and heuristic search. Ann. Oper. Res. 86, 473–490 (1997)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Merz, P., Freisleben, B.: Fitness landscape analysis and memetic algorithms for the quadratic assignment problem. Trans. Evol. Comput 4(4), 337–352 (2000). ISSN 1089–778XGoogle Scholar
  8. 8.
    Rendell, P.: Chapter 26–A simple universal turing machine for the game of life turing machine. In: Adamatzky, A. (ed.) Game of Life Cellular Automata, pp. 519–545. Springer, London (2010)CrossRefGoogle Scholar
  9. 9.
    HP laptop with a 2.67 GHz Dual Core 64bit Intel processor and 3 Gb of RAM running Windows 7Google Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Department of Computer ScienceUniversity of the West of EnglandBristolUK

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