Soliton Automata with Multiple Waves

  • Henning Bordihn
  • Helmut JürgensenEmail author
  • Heiko Ritter
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8808)


Soliton automata were defined by Dassow and Jürgensen about 1986 to model the changes of the bond structure in certain types of molecules as a result of a soliton wave travelling through the molecules. We extend the model to include the presence of more than just a single soliton. Certain situations are specific to the multi-soliton case and lead to changes to some of the basic definitions and result in a new class of soliton automata. In this paper we lay the foundations for a theory of multi-soliton automata, explain the modelling decisions, and discuss issues which are new when multiple solitons are considered.


Cellular Automaton Weighted Graph Naval Research Laboratory Interior Node Input Symbol 
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  1. 1.
    Bartha, M., Jürgensen, H.: Characterizing finite undirected multigraphs as indexed algebras. Technical Report Report 252, Department of Computer Science, The University of Western Ontario (1989)Google Scholar
  2. 2.
    Bartha, M., Krész, M.: Elementary decomposition of soliton automata. Acta Cybernet. 14, 631–652 (2000)MathSciNetzbMATHGoogle Scholar
  3. 3.
    Bartha, M., Krész, M.: Structuring the elementary components of graphs having perfect internal matching. Theoret. Comput. Sci. 299, 179–210 (2003)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Bartha, M., Krész, M.: Deterministic soliton graphs. Informatica 30, 281–288 (2006)MathSciNetzbMATHGoogle Scholar
  5. 5.
    Bartha, M., Krész, M.: Splitters and barriers in open graphs having a perfect internal matching. Acta Cybernet. 18, 697–718 (2008)MathSciNetzbMATHGoogle Scholar
  6. 6.
    Bartha, M., Krész, M.: Deciding the deterministic property for soliton graphs. Ars Math. Contemp. 2, 121–136 (2009)MathSciNetzbMATHGoogle Scholar
  7. 7.
    Bartha, M., Krész, M.: Soliton circuits and network-based automata: Review and perspectives. In: Martín-Vide, C. (ed.) Scientific Applications of Language Methods Mathematics, Computing, Language, and Life: Frontiers in Mathematical Linguistics and Language Theory, vol. 2, pp. 585–631. Imperial College Press, London (2011)Google Scholar
  8. 8.
    Carter, F.L.: Conformational switching at the molecular level. In: Carter, F.L. (ed.) Molecular Electronic Devices, pp. 51–71. Marcel Dekker, New York (1982)Google Scholar
  9. 9.
    Carter, F.L.: The concepts of molecular electronics. In: Aizawa, M. (ed.) Bioelectronics. Research and Development Report, vol. 50, pp. 123–158. CMC Press, Denver (1984)Google Scholar
  10. 10.
    Carter, F.L.: The molecular device computer: Point of departure for large scale cellular automata. In: Farmer, D., Toffoli, T., Wolfram, S. (eds.) Cellular Automtata, Proceedings of an Interdisciplinary Workshop, pp. 175–194. North-Holland, Amsterdam (1983,1984); Published in Physica 10D(1&2)Google Scholar
  11. 11.
    Carter, F.L., Schultz, A., Duckworth, D.: Soliton switching and its implications for molecular electronics. In: Carter [17], pp. 149–182Google Scholar
  12. 12.
    Carter, F.L.: Problems and prospects of future electroactive polymers and “molecular” electronic devices. In: Lockhart, L.B. (ed.) The NRL Program on Electroactive Polymers, First Annual Report. NRL Memorandum Report, vol. 3960, pp. 121–175. Naval Research Laboratory, Washington (1979)Google Scholar
  13. 13.
    Carter, F.L.: Further considerations on “molecular” electronic devices. In: Fox, R.B. (ed.): The NRL Program on Electroactive Polymers, Second Annual Report. NRL Memorandum Report, vol. 4335, pp. 35–52. Naval Research Laboratory, Washington (1980)Google Scholar
  14. 14.
    Carter, F.L.: Searching for S-P analogues of (SN)\(_{\rm {x}}\). In: Fox, R.B. (ed.) The NRL Program on Electroactive Polymers, Second Annual Report. NRL Memorandum Report, vol. 4335, pp. 3–10. Naval Research Laboratory, Washington (1980)Google Scholar
  15. 15.
    Carter, F.L.: The chemistry in future molecular computers. In: Heller, S.R., Potenzone, Jr., S.R. (eds.) Proceedings of the 6th International Conference on Computers in Chemical Research and Education (ICCCRE) Computer Applications in Chemistry. Held in Washington, DC, July 11–16, 1982. Analytical Chemistry Symposia Series, vol. 15, pp. 225–262. Elsevier, Amsterdam (1983)Google Scholar
  16. 16.
    Carter, F.L.: Molecular level fabrication techniques and molecular electronic devices. J. Vac. Sci. Technol. B 1(4), 959–968 (1983)CrossRefGoogle Scholar
  17. 17.
    Carter, F.L. (ed.): Molecular Electronic Devices II. Marcel Dekker, New York (1987)Google Scholar
  18. 18.
    Dassow, J., Jürgensen, H.: Soliton automata. J. Comput. System Sci. 40, 158–181 (1990)MathSciNetCrossRefzbMATHGoogle Scholar
  19. 19.
    Dassow, J., Jürgensen, H.: Deterministic soliton automata with a single exterior node. Theoret. Comput. Sci. 84, 281–292 (1991)MathSciNetCrossRefzbMATHGoogle Scholar
  20. 20.
    Dassow, J., Jürgensen, H.: Deterministic soliton automata with at most one cycle. J. Comput. System Sci. 46, 155–197 (1993)MathSciNetCrossRefzbMATHGoogle Scholar
  21. 21.
    Dassow, J., Jürgensen, H.: The transition monoids of soliton trees. In: Păun, G. (ed.) Mathematical Linguistics and Related Topics. Papers in Honour of Solomon Marcus on His 70th Birthday, pp. 76–87, Editura Academiei Române, Bucureşti (1995)Google Scholar
  22. 22.
    Davydov, A.S.: Solitons in Molecular Systems. D. Reidel Publ. Co., (1985)Google Scholar
  23. 23.
    Groves, M.P.: Dynamic circuit diagrams for some soliton switching devices. In: Carter [17], pp. 183–204Google Scholar
  24. 24.
    Groves, M.P.: Towards verification of soliton circuits. In: Carter, F.L., Siatkowski, R.E., Wohltjen, H. (eds.) Molecular Electronic Devices, pp. 287–302. North-Holland, Amsterdam (1988)Google Scholar
  25. 25.
    Groves, M.P.: Soliton circuit design using molecular gate arrays. In: Kotagiri, R., Patel, M. (eds.) Proceedings of the Twentieth Australasian Computer Science Conference, ACSC 1997, Sydney, Australia, pp. 245–252 (February 5–7, 1997), Published in Australian Computer Science Communications 19(1)Google Scholar
  26. 26.
    Groves, M.P., Carvalho, C.F., Marlin, C.D., Prager, R.H.: Using soliton circuits to build molecular memories. Australian Computer Science Communications 15(1), 37–45 (1993); This journal issue contains the “Proceedings of the Sixteenth Australian Computer Science Conference, ACSC-16, February 3–5, 1993, Brisbane, Queensland”, edited by G. Gupta, G. Mohay and R. ToporGoogle Scholar
  27. 27.
    Groves, M.P., Carvalho, C.F., Prager, R.H.: Switching the polyacetylene soliton. Materials Science and Engineering C3, 181–185 (1995)CrossRefGoogle Scholar
  28. 28.
    Groves, M.P., Marlin, C.D.: Using soliton circuits to build molecular computers. Australian Computer Science Communications 17, 188–193 (1995)Google Scholar
  29. 29.
    Groves, M.P.: A Soliton Circuit Design System. PhD Thesis, University of Adelaide (1987)Google Scholar
  30. 30.
    Hashmall, J.A., Baker, L.C.W., Carter, F.L., Brant, P., Weber, D.C.: Semi-empirical calculations on electroactive polymeres. In: Fox, R.B. (ed.) The NRL Program on Electroactive Polymers, Second Annual Report. NRL Memorandum Report, vol. 4335, pp. 11–23. Naval Research Laboratory, Washington (1980)Google Scholar
  31. 31.
    Jürgensen, H., Kraak, P.: Soliton automata based on trees. Internat. J. Foundations Comput. Sci. 18, 1257–1270 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  32. 32.
    Krész, M.: Soliton Automata: A Computational Model on the Principle of Graph Matchings. PhD thesis, University of Szeged, Hungary (2004)Google Scholar
  33. 33.
    Krész, M.: Simulation of Soliton Circuits. In: Farré, J., Litovsky, I., Schmitz, S. (eds.) CIAA 2005. LNCS, vol. 3845, pp. 347–348. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  34. 34.
    Krész, M.: Graph decomposition and descriptional complexity of soliton automata. J. of Automata, Languages and Combinatorics 12, 237–263 (2007)MathSciNetzbMATHGoogle Scholar
  35. 35.
    Krész, M.: Soliton automata with constant external edges. Theoret. Comput. Sci. 206, 1126–1141 (2008)MathSciNetzbMATHGoogle Scholar
  36. 36.
    Lu, Y.: Solitons & Polarons in Conducting Polymers. World Scientific, Singapore (1988)Google Scholar
  37. 37.
    Does molecular electronics compute? Nature Nanotechnology 8(6) (2013), 377. EditorialGoogle Scholar
  38. 38.
    Park, J.K., Steiglitz, K., Thurston, W.P.: Soliton-like behavior in automata. Physica 19D, 423–432 (1986)MathSciNetzbMATHGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Henning Bordihn
    • 1
  • Helmut Jürgensen
    • 2
    Email author
  • Heiko Ritter
    • 1
  1. 1.Institut für InformatikUniversität PotsdamPotsdamGermany
  2. 2.Department of Computer ScienceWestern UniversityLondonCanada

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