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Turing Computability and Membrane Computing

  • Yurii Rogozhin
  • Artiom Alhazov
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7762)

Abstract

Alan Turing began a new area in science; he discovered that there are universal computers, which in principal are very simple. Up to now this is the basis of a modern computing theory and practice. In the paper one considers Turing computability in the frame of P (membrane) systems and other distributive systems. An overview of the recent results about small universal P and DNA systems and some open problems and possible directions of investigation are presented.

Keywords

Turing Machine Communication Graph Register Machine Membrane Computing Formal Language Theory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Adleman, L.: Molecular Computation of Solutions to Combinatorial Problems. Science 226, 1021–1024 (1994)CrossRefGoogle Scholar
  2. 2.
    Alhazov, A., Freund, R., Rogozhin, Y.: Computational Power of Symport/Antiport: History, Advances, and Open Problems. In: Freund, R., Păun, G., Rozenberg, G., Salomaa, A. (eds.) WMC 2005. LNCS, vol. 3850, pp. 1–30. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  3. 3.
    Alhazov, A., Krassovitskiy, A., Rogozhin, Y.: Circular Post Machines and P Systems with Exo-insertion and Deletion. In: Gheorghe, M., Păun, G., Rozenberg, G., Salomaa, A., Verlan, S. (eds.) CMC 2011. LNCS, vol. 7184, pp. 73–86. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  4. 4.
    Alhazov, A., Kogler, M., Margenstern, M., Rogozhin, Y., Verlan, S.: Small Universal TVDH and Test Tube Systems. International Journal of Foundations of Computer Science 22(1), 143–154 (2011)MathSciNetMATHCrossRefGoogle Scholar
  5. 5.
    Alhazov, A., Kudlek, M., Rogozhin, Y.: Nine Universal Circular Post Machines. Computer Science Journal of Moldova 10, 3(30), 247–262 (2002)MathSciNetGoogle Scholar
  6. 6.
    Alhazov, A., Rogozhin, Y., Verlan, S.: A Small Universal Splicing P System. In: Gheorghe, M., Hinze, T., Păun, G., Rozenberg, G., Salomaa, A. (eds.) CMC 2010. LNCS, vol. 6501, pp. 95–102. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  7. 7.
    Alhazov, A., Rogozhin, Y., Verlan, S.: On Small Universal Splicing Systems. Fundamenta Informaticae (in press)Google Scholar
  8. 8.
    Alhazov, A., Verlan, S.: Minimization Strategies for Maximally Parallel Multiset Rewriting Systems. TUCS Report No. 862 (2008), and arXiv:1009.2706v1 [cs.FL], and Theoretical Computer Science 412, 1581–1591 (2011)Google Scholar
  9. 9.
    Cocke, J., Minsky, M.: Universality of Tag Systems with P = 2. Journal of the Association for Computing Machinery 11(1), 15–20 (1964)MathSciNetMATHCrossRefGoogle Scholar
  10. 10.
    Csuhaj-Varjú, E., Kari, L., Păun, G.: Test Tube Distributed Systems Based on Splicing. Computers and Artificial Intelligence 15(2–3), 211–232 (1996)MathSciNetMATHGoogle Scholar
  11. 11.
    Csuhaj-Varjú, E., Margenstern, M., Vaszil, G., Verlan, S.: Small Computationally Complete Symport/Antiport P systems. Theoretical Computer Science 372(2-3), 152–164 (2007)MathSciNetMATHCrossRefGoogle Scholar
  12. 12.
    Csuhaj-Varjú, E., Verlan, S.: On Length-Separating Test Tube Systems. Natural Computing 7(2), 167–181 (2008)MathSciNetMATHCrossRefGoogle Scholar
  13. 13.
    Freund, R., Alhazov, A., Rogozhin, Y., Verlan, S.: Communication P Systems. In: Păun, G., Rozenberg, G., Salomaa, A. (eds.) The Oxford Handbook of Membrane Computing, ch. 5, pp. 118–143 (2010)Google Scholar
  14. 14.
    Freund, F., Freund, R.: Test Tube Systems: When Two Tubes are Enough. In: Rozenberg, G., Thomas, W. (eds.) Developments in Language Theory, Foundations, Applications and Perspectives, pp. 338–350. World Scientific Publishing Co., Singapore (2000)Google Scholar
  15. 15.
    Frisco, P., Zandron, C.: On Variants of Communicating Distributed H Systems. Fundamenta Informaticae 48(1), 9–20 (2001)MathSciNetMATHGoogle Scholar
  16. 16.
    Frisco, P.: Computing with Cells: Advances in Membrane Computing. Oxford University Press (2009)Google Scholar
  17. 17.
    Head, T.: Formal Language Theory and DNA: An Analysis of the Generative Capacity of Recombinant Behaviors. Bulletin of Mathematical Biology 49, 737–759 (1987)MathSciNetMATHGoogle Scholar
  18. 18.
    Head, T., Păun, G., Pixton, D.: Language Theory and Molecular Genetics. Generative Mechanisms Suggested by DNA Recombination. In: [41], ch. 7, vol. 2Google Scholar
  19. 19.
    Korec, I.: Small Universal Register Machines. Theoretical Computer Science 168, 267–301 (1996)MathSciNetMATHCrossRefGoogle Scholar
  20. 20.
    Lipton, R.J.: DNA Solution of Hard Computational Problems. Science 268, 542–545 (1995)CrossRefGoogle Scholar
  21. 21.
    Margenstern, M.: Frontier Between Decidability and Undecidability: A Survey. Theoretical Computer Science 231(2), 217–251 (2000)MathSciNetMATHCrossRefGoogle Scholar
  22. 22.
    Margenstern, M.: Surprising Areas in the Quest for Small Universal Devices. Electronic Notes in Theoretical Computer Science 225, 201–220 (2009)CrossRefGoogle Scholar
  23. 23.
    Margenstern, M., Pavlotskaya, L.: On the Optimal Number of Instructions for Universality of Turing Machines Connected with a Finite Automaton. International Journal of Algebra and Computation 13(2), 133–202 (2003)MathSciNetMATHCrossRefGoogle Scholar
  24. 24.
    Margenstern, M., Rogozhin, Y.: A universal time-varying distributed H system of degree 1. In: Jonoska, N., Seeman, N.C. (eds.) DNA 2001. LNCS, vol. 2340, pp. 371–380. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  25. 25.
    Margenstern, M., Rogozhin, Y., Verlan, S.: Time-Varying Distributed H Systems of Degree 2 Can Carry Out Parallel Computations. In: Hagiya, M., Ohuchi, A. (eds.) DNA 2002. LNCS, vol. 2568, pp. 326–336. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  26. 26.
    Chen, J., Reif, J.H. (eds.): DNA 2003. LNCS, vol. 2943, pp. 48–53. Springer, Heidelberg (2004)MATHCrossRefGoogle Scholar
  27. 27.
    Margenstern, M., Verlan, S., Rogozhin, Y.: Time-varying distributed H systems: an overview. Fundamenta Informaticae 64, 291–306 (2005)MathSciNetMATHGoogle Scholar
  28. 28.
    Minsky, M.: Computation, Finite and Infinite Machines. Prentice-Hall, Englewood Cliffs (1967)MATHGoogle Scholar
  29. 29.
    De Mol, L.: Tag Systems and Collatz-like Functions. Theoretical Computer Science 390, 92–101 (2008)MathSciNetMATHCrossRefGoogle Scholar
  30. 30.
    Neary, T., Woods, D.: The Complexity of Small Universal Turing Machines: A Survey. In: Bieliková, M., Friedrich, G., Gottlob, G., Katzenbeisser, S., Turán, G. (eds.) SOFSEM 2012. LNCS, vol. 7147, pp. 385–405. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  31. 31.
    Pavlotskaya, L.: Solvability of the Halting Problem for Certain Classes of Turing Machines. Mathematical Notes 13(6), 537–541 (1973); Translated from Matematicheskie Zametki 13(6), 899–909 (1973)MATHCrossRefGoogle Scholar
  32. 32.
    Păun, G.: Computing with Membranes. Journal of Computer and System Sciences 1(61), 108–143 (2000); Also TUCS Report No. 208 (1998)CrossRefGoogle Scholar
  33. 33.
    Păun, G., Yokomori, T.: Membrane Computing Based on Splicing. In: Winfree, E., Gifford, D.K. (eds.) DNA Based Computers V. DIMACS Series in Discrete Mathematics and Theoretical Computer Science, vol. 54, pp. 217–232. American Mathematical Society (1999)Google Scholar
  34. 34.
    Păun, G., Rozenberg, G., Salomaa, A.: DNA Computing: New Computing Paradigms. Springer, Heidelberg (1998)MATHCrossRefGoogle Scholar
  35. 35.
    Păun, G., Rozenberg, G., Salomaa, A. (eds.): The Oxford Handbook of Membrane Computing. Oxford University Press (2010)Google Scholar
  36. 36.
    Post, E.L.: Formal Reductions of the General Combinatorial Decision Problem. American Journal of Mathematics 65(2), 197–215 (1943)MathSciNetMATHCrossRefGoogle Scholar
  37. 37.
    Priese, L., Rogozhin, Y., Margenstern, M.: Finite H-systems with 3 Test Tubes are not Predictable. In: Altman, R., Dunker, A., Hanter, L., Klein, T. (eds.) Proceedings of Pacific Simposium on Biocomputing, pp. 545–556. World Sci.Publ., Singapore (1998)Google Scholar
  38. 38.
    Robinson, R.M.: Minsky’s Small Universal Turing Machine. International Journal of Mathematics 2(5), 551–562 (1991)MathSciNetMATHCrossRefGoogle Scholar
  39. 39.
    Rogozhin, Y.: Small Universal Turing Machines. Theoretical Computer Science 168(2), 215–240 (1996)MathSciNetMATHCrossRefGoogle Scholar
  40. 40.
    Rogozhin, Y., Verlan, S.: On the Rule Complexity of Universal Tissue P Systems. In: Freund, R., Păun, G., Rozenberg, G., Salomaa, A. (eds.) WMC 2005. LNCS, vol. 3850, pp. 356–362. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  41. 41.
    Rozenberg, G., Salomaa, A.: Handbook of Formal Languages, vol. 3. Springer, Heidelberg (1997)MATHCrossRefGoogle Scholar
  42. 42.
    Shannon, C.E.: A Universal Turing Machines with Two Internal States. Automata Studies, Ann. of Math. Stud. 34, 157–165 (1956)MathSciNetGoogle Scholar
  43. 43.
    Turing, A.M.: On Computable Real Numbers, with an Application to the Entscheidungsproblem. Proc. London Math. Soc. Ser. 2 42, 230–265 (1936)CrossRefGoogle Scholar
  44. 44.
    Verlan, S.: A Boundary Result on Enhanced Time-Varying Distributed H Systems with Parallel Computations. Theoretical Computer Science 344(2-3), 226–242 (2005)MathSciNetMATHCrossRefGoogle Scholar
  45. 45.
    Verlan, S.: Communicating Distributed H Systems with Alternating Filters. In: Jonoska, N., Păun, G., Rozenberg, G. (eds.) Aspects of Molecular Computing. LNCS, vol. 2950, pp. 367–384. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  46. 46.
    Verlan, S.: Head Systems and Application to Bio-Informatics. PhD thesis, LITA, Université de Metz, Metz, France (2004)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Yurii Rogozhin
    • 1
  • Artiom Alhazov
    • 1
  1. 1.Institute of Mathematics and Computer ScienceAcademy of Sciences of MoldovaChişinc̆auMoldova

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