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Collision-Based Computing

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Handbook of Natural Computing

Abstract

Collision-based computing is an implementation of logical circuits, mathematical machines, or other computing and information processing devices in homogeneous, uniform and unstructured media with traveling mobile localizations. A quanta of information is represented by a compact propagating pattern (gliders in cellular automata, solitons in optical systems, wave fragments in excitable chemical systems). Logical truth corresponds to presence of the localization, logical false to absence of the localization; logical values can also be represented by a particular state of the localization. When two or more traveling localizations collide, they change their velocity vectors and/or states. Post-collision trajectories and/or states of the localizations represent results of logical operations implemented by the collision. One of the principal advantages of the collision-based computing medium – hidden in 1D systems but obvious in 2D and 3D media – is that the medium is architecture-less: nothing is hardwired, there are no stationary wires or gates, a trajectory of a propagating information quanta can be seen as a momentary wire. The basics of collision-based computing are introduced, and the collision-based computing schemes in 1D and 2D cellular automata and continuous excitable media are overviewed. Also a survey of collision-based schemes, where particles/collisions are dimensionless, is provided.

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References

  • Adamatzky A (ed) (2002a) Collision-based computing. Springer, London

    MATH  Google Scholar 

  • Adamatzky A (ed) (2002b) Novel materials for collision-based computing. Springer, Berlin

    Book  Google Scholar 

  • Adamatzky A (2004) Collision-based computing in Belousov–Zhabotinsky medium. Chaos Soliton Fract 21:1259–1264

    Article  MATH  Google Scholar 

  • Adamatzky A, De Lacy Costello B (2007) Binary collisions between wave-fragments in sub-excitable Belousov–Zhabotinsky medium. Chaos Soliton Fract 34:307–315

    Article  MATH  Google Scholar 

  • Adamatzky A, Wuensche A (2007) Computing in spiral rule reaction-diffusion hexagonal cellular automaton. Complex Syst 16(4):277–298

    Google Scholar 

  • Adamatzky A, Wuensche A, De Lacy Costello B (2006) Glider-based computation in reaction-diffusion hexagonal cellular automata. Chaos Soliton Fract 27:287–295

    Article  MATH  Google Scholar 

  • Anastassiou C, Fleischer JW, Carmon T, Segev M, Steiglitz K (2001) Information transfer via cascaded collisions of vector solitons. Optics Lett 26:1498–1500

    Article  Google Scholar 

  • Atrubin AJ (1965) A one-dimensional real-time iterative multiplier. IEEE Trans Electron Computers EC-14(1):394–399

    Article  Google Scholar 

  • Banks E (1971) Information and transmission in cellular automata. Ph.D Dissertation, MIT, cited by Toffoli and Margolus (1987)

    Google Scholar 

  • Beato V, Engel H (2003) Pulse propagation in a model for the photosensitive Belousov-Zhabotinsky reaction with external noise. In: Schimansky-Geier L, Abbott D, Neiman A, van den Broeck C (eds) Noise in complex systems and stochastic dynamics. Proceedings of SPIE, 2003

    Google Scholar 

  • Berlekamp ER, Conway JH, Guy RL (1982) Winning ways for your mathematical plays, vol 2 Games in particular. Academic, London

    MATH  Google Scholar 

  • Blum L, Cucker F, Shub M, Smale S (1998) Complexity and real computation. Springer, New York

    Google Scholar 

  • Boccara N, Nasser J, Roger M (1991) Particle-like structures and interactions in spatio-temporal patterns generated by one-dimensional deterministic cellular automaton rules. Phys Rev A 44(2):866–875

    Article  Google Scholar 

  • Cook M (2004) Universality in elementary cellular automata. Complex Syst 15:1–40

    MATH  Google Scholar 

  • Das R, Crutchfield JP, Mitchell M, Hanson JE (1995) Evolving globally synchronized cellular automata. In: Eshelman LJ (ed) International conference on genetic algorithms '95. Morgan Kaufmann, San Mateo, CA, pp 336–343

    Google Scholar 

  • Delorme M, Mazoyer J (2002) Signals on cellular automata. In: Adamatzky A (ed) Collision-based computing. Springer, Berlin, pp 234–275

    Google Scholar 

  • Durand-Lose J (1996) Grain sorting in the one dimensional sand pile model. Complex Syst 10(3):195–206

    MathSciNet  MATH  Google Scholar 

  • Durand-Lose J (1998) Parallel transient time of one-dimensional sand pile. Theoret Comp Sci 205(1–2):183–193

    Article  MathSciNet  MATH  Google Scholar 

  • Durand-Lose J (2007) Abstract geometrical computation and the linear Blum, Shub and Smale model. In: Cooper S, Löwe B, Sorbi A (eds) Computation and logic in the real world. 3rd Conference Computability in Europe (CiE '07). Springer, no. 4497 in LNCS, pp 238–247

    Google Scholar 

  • Durand-Lose J (2008a) Abstract geometrical computation: small Turing universal signal machines. In: Neary T, Seda A, Woods D (eds) International workshop on the complexity of simple programs. Cork University Press, Cork, Ireland, December 6–7

    Google Scholar 

  • Durand-Lose J (2008b) Abstract geometrical computation with accumulations: beyond the Blum, Shub and Smale model. In: Beckmann A, Dimitracopoulos C, Löwe B (eds) Logic and theory of algorithms. CiE 2008 (abstracts and extended abstracts of unpublished papers). University of Athens, Athens, pp 107–116

    Google Scholar 

  • Durand-Lose J (2009) Abstract geometrical computation 3: Black holes for classical and analog computing. Nat Comput 8(3):455–472

    Google Scholar 

  • Etesi G, Németi I (2002) Non-Turing computations via Malament-Hogarth space-times. Int J Theor Phys 41(2):341–370, gr-qc/0104023

    Article  MATH  Google Scholar 

  • Field RJ, Noyes RM (1974) Oscillations in chemical systems. iv. limit cycle behavior in a model of a real chemical reaction. J Chem Phys 60:1877–1884

    Article  Google Scholar 

  • Fischer PC (1965) Generation of primes by a one-dimensional real-time iterative array. J ACM 12(3):388–394

    Article  MATH  Google Scholar 

  • Fredkin EF, Toffoli T (1982) Conservative logic. Int J Theor Phys 21(3/4)219–253

    Article  MathSciNet  MATH  Google Scholar 

  • Fredkin EF, Toffoli T (2002) Design principles for achieving high-performance submicron digital technologies. In: Adamatzky A (ed) Collision-based computing. Springer, Berlin, pp 27–46

    Google Scholar 

  • Hogarth ML (1994) Non-Turing computers and non-Turing computability. In: Hull D, Forbens M, Burian RM (eds) Biennial meeting of the philosophy of science association. East Lansing, MI, pp 126–138

    Google Scholar 

  • Ilachinski A (2001) Cellular automata – a discrete universe. World Scientific, Singapore

    MATH  Google Scholar 

  • Jakubowski MH, Steiglitz K, Squier RK (1996) When can solitons compute? Complex Syst 10(1):1–21

    MathSciNet  MATH  Google Scholar 

  • Jakubowski MH, Steiglitz K, Squier RK (2001) Computing with solitons: a review and prospectus. Multiple Valued Logic 6(5–6):439–462

    MathSciNet  MATH  Google Scholar 

  • Kari J (2005) Theory of cellular automata: a survey. Theoret Comp Sci 334:3–33

    Article  MathSciNet  MATH  Google Scholar 

  • Krug HJ, Pohlmann L, Kuhnert L (1990) Analysis of the modified complete oregonator (MCO) accounting for oxygen- and photosensitivity of Belousov-Zhabotinsky systems. J Phys Chem 94:4862–4866

    Article  Google Scholar 

  • Lindgren K, Nordahl MG (1990) Universal computation in simple one-dimensional cellular automata. Complex Syst 4:299–318

    MathSciNet  MATH  Google Scholar 

  • Lloyd S, Ng YJ (2004) Black hole computers. Sci Am 291(5):31–39

    Article  Google Scholar 

  • Margolus N (1984) Physics-like models of computation. Phys D 10:81–95

    Article  MathSciNet  Google Scholar 

  • Mazoyer J (1996) Computations on one dimensional cellular automata. Ann Math Artif Intell 16:285–309

    Article  MathSciNet  MATH  Google Scholar 

  • Neary T, Woods D (2009) Four fast universal Turing machines. Fundam Inform 410(4):443–450

    MathSciNet  MATH  Google Scholar 

  • Ollinger N (2002) The quest for small universal cellular automata. In: ICALP '02, Springer, Heidelberg, no. 2380 in LNCS, pp 318–329

    Google Scholar 

  • Rand D, Steiglitz K (2009) Computing with solitons. In: Meyers RA (ed) Encyclopedia of complexity and systems science. Springer, Heidelberg

    Google Scholar 

  • Rand D, Steiglitz K, Prucnal P (2005) Signal standardization in collision-based soliton computing. Int J Unconvent Comput 1:31–45

    Google Scholar 

  • Rendell P (2002) Turing universality of the game of life. In: Adamatzky A (ed) Collision-based computing. Springer, Berlin, pp 513–540

    Google Scholar 

  • Rennard JP (2002) Implementation of logical functions in the game of life. In: Adamatzky A (ed) Collision-based computing. Springer, London, pp 491–512

    Chapter  Google Scholar 

  • Richard G, Ollinger N (2008) A particular universal cellular automaton. In: Neary T, Woods D, Seda AK, Murphy N (eds) The complexity of simple programs. National University of Ireland, Cork

    Google Scholar 

  • Sarkar P (2000) A brief history of cellular automata. ACM Comput Surv 32(1):80–107

    Article  Google Scholar 

  • Sendiña-Nadal I, Mihaliuk E, Wang J, Pérez-Muñuzuri V, Showalter K (2001) Wave propagation in subexcitable media with periodically modulated excitability. Phys Rev Lett 86:1646–1649

    Article  Google Scholar 

  • Steiglitz K (2001) Time-gated Manakov spatial solitons are computationally universal. Phys Rev E 63:1660–1668

    Article  Google Scholar 

  • Toffoli T, Margolus N (1987) Cellular automata machine - a new environment for modeling. MIT Press, Cambridge, MA

    Google Scholar 

  • Tyson JJ, Fife PC (1980) Target patterns in a realistic model of the Belousov-Zhabotinsky reaction. J Chem Phys 73:2224–2237

    Article  MathSciNet  Google Scholar 

  • Waksman A (1966) An optimum solution to the firing squad synchronization problem. Inform Control 9(1):66–78

    Article  MathSciNet  MATH  Google Scholar 

  • Woods D, Neary T (2006) On the time complexity of 2-tag systems and small universal Turing machines. In: 47th Annual IEEE Symposium on Foundations of Computer Science (FOCS '06), IEEE Computer Society, Berkeley, CA, pp 439–448

    Chapter  Google Scholar 

  • Wuensche A (2005) Glider dynamics in 3-value hexagonal cellular automata: the beehive rule. Int J Unconventional Comput 1:375–398

    Google Scholar 

  • Wuensche A, Adamatzky A (2006) On spiral glider-guns in hexagonal cellular automata: activator-inhibitor paradigm. Int J Modern Phys C 17(7):1009–1026

    Article  MATH  Google Scholar 

  • Yunès JB (2007a) Automates cellulaires; fonctions booléennes. Habilitation à diriger des recherches, Université Paris 7

    Google Scholar 

  • Yunès JB (2007b) Simple new algorithms which solve the firing squad synchronization problem: a 7-states 4n-steps solution. In: Durand-Lose J, Margenstern M (eds) Machine, Computations and Universality (MCU '07). Springer, Berlin, no. 4664 in LNCS, pp 316–324

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Computer Science, University of the West of England, Bristol, UK

    Andrew Adamatzky

  2. LIFO, Université d'Orléans, Orléans, France

    Jérôme Durand-Lose

Authors
  1. Andrew Adamatzky
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  2. Jérôme Durand-Lose
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Editor information

Editors and Affiliations

  1. LIACS, Leiden University, Leiden, The Netherlands

    Grzegorz Rozenberg

  2. Computer Science Department, University of Colorado, Boulder, USA

    Grzegorz Rozenberg

  3. LIACS, Leiden University, Leiden, The Netherlands

    Thomas Bäck

  4. LIACS, Leiden University, Leiden, The Netherlands

    Joost N. Kok

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Adamatzky, A., Durand-Lose, J. (2012). Collision-Based Computing. In: Rozenberg, G., Bäck, T., Kok, J.N. (eds) Handbook of Natural Computing. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-92910-9_58

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