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Some Open Problems about Catalytic, Numerical, and Spiking Neural P Systems

(Extended Abstract)
  • Gheorghe Păun
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8340)

Abstract

Some open problems and research topics are pointed, about three classes of P systems: catalytic, numerical, and spiking neural P systems. In each case, several issues are briefly discussed, in general, related to questions already formulated as open problems in the literature and also related to recent results dealing with these questions.

Keywords

Open Problem Membrane Computing Formal Language Theory Spike Neural Splice System 
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.
    Binder, A., Freund, R., Oswald, M., Vock, L.: Extended spiking neural P systems with excitatory and inhibitory astrocytes. In: Proc. Eighth WSEAS Intern. Conf. on Evolutionary Computing, pp. 320–325. Vancouver, Canada (2007)Google Scholar
  2. 2.
    Calude, C., Păun, G.: Bio-steps beyond Turing. BioSystems 77, 175–194 (2004)Google Scholar
  3. 3.
    Csuhaj-Varjú, E., Dassow, J., Kelemen, J., Păun, G.: Grammar Systems. In: A Grammatical Approach to Distribution and Cooperation, Gordon and Breach, London (1994)Google Scholar
  4. 4.
    Chen, H., Ishdorj, T.-O., Păun, G.: Computing along the axon. Progress in Natural Science 17(4), 418–423 (2007)Google Scholar
  5. 5.
    Chen, H., Ishdorj, T.-O., Păun, G., Pérez-Jiménez, M.J.: Spiking neural P systems with extended rules. In: Proc. Fourth Brainstorming Week on Membrane Computing, Sevilla, RGNC Report 02/2006, pp. 241–265 (2006)Google Scholar
  6. 6.
    Dassow, J., Păun, G.: Regulated Rewriting in Formal Language Theory. Springer, Berlin (1989)Google Scholar
  7. 7.
    Freund, R.: Particular results for variants of P systems with one catalyst in one membrane. In: Proc. Fourth Brainstorming Week on Membrane Computing, vol. II, pp. 41–50. Fénix Editora, Sevilla (2006)Google Scholar
  8. 8.
    Freund, R.: Purely catalytic P systems: Two catalysts can be sufficient for computational completeness. In the present volumeGoogle Scholar
  9. 9.
    Freund, R., Ibarra, O.H., Păun, A., Sosík, P., Yen, H.-C.: Catalytic P systems. In: [33], ch. 4Google Scholar
  10. 10.
    Freund, R., Kari, L., Oswald, M., Sosík, P.: Computationally universal P systems without priorities: two catalysts are sufficient. Theoretical Computer Science 330, 251–266 (2005)CrossRefzbMATHMathSciNetGoogle Scholar
  11. 11.
    Freund, R., Păun, G.: Universal P systems: One catalyst can be sufficient. In: Proc. 11th Brainstorming Week on Membrane Computing, February 4-8, Fénix Editora, Sevilla (2013)Google Scholar
  12. 12.
    Gheorghe, M., Păun, G., Pérez-Jiménez, M.J., Rozenberg, G.: Frontiers of membrane computing: Open problems and research topics. Intern. J. Found. Computer Sci. (2013) (first version in Proc. Tenth Brainstorming Week on Membrane Computing, vol. I, Sevilla, January 30-February 3, pp. 171–249 (2012))Google Scholar
  13. 13.
    Ibarra, O.H., Dang, Z., Egecioglu, O.: Catalytic P systems, semilinear sets, and vector addition systems. Th. Computer Sci. 312, 379–399 (2004)CrossRefzbMATHMathSciNetGoogle Scholar
  14. 14.
    Ibarra, O.H., Dang, Z., Egecioglu, O., Saxena, G.: Characterizations of catalytic membrane computing systems. In: Rovan, B., Vojtáš, P. (eds.) MFCS 2003. LNCS, vol. 2747, pp. 480–489. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  15. 15.
    Ionescu, M., Păun, G.: Notes about spiking neural P systems. In: Proc. Ninth Brainstorming Week on Membrane Computing, January 31-February 4, pp. 169–182. Fénix Editora, Sevilla (2011)Google Scholar
  16. 16.
    Ionescu, M., Păun, G., Pérez-Jiménez, M.J., Yokomori, T.: Spiking neural dP systems. Fundamenta Informaticae 11(4), 423–436 (2011)Google Scholar
  17. 17.
    Ionescu, M., Păun, G., Yokomori, T.: Spiking neural P systems. Fundamenta Informaticae 71(2-3), 279–308 (2006)Google Scholar
  18. 18.
    Krishna, S.N., Păun, A.: Results on catalytic and evolution-communication P systems. New Generation Computing 22, 377–394 (2004)CrossRefzbMATHGoogle Scholar
  19. 19.
    Krithivasan, K., Păun, G., Ramanujan, A.: On controlled P systems. In: Fundamenta Informaticae (to appear)Google Scholar
  20. 20.
    Leporati, A., Porreca, A.E., Zandron, C., Mauri, G.: Improving universality results on parallel enzymatic numerical P systems. In: Proc. 11th Brainstorming Week on Membrane Computing, February 4-8, Fénix Editora, Sevilla (2013)Google Scholar
  21. 21.
    Leporati, A., Mauri, G., Porreca, A.E., Zandron, C.: Enzymatic numerical P systems using elementary arithmetic operations. In: Alhazov, A., Cojocaru, S., Gheorghe, M., Rogozhin, Y., Rozenberg, G., Salomaa, A. (eds.) CMC 2013, vol. 8340, pp. 249–264. Springer, Heidelberg (2014)Google Scholar
  22. 22.
    Mutyam, M., Krithivasan, K.: P systems with membrane creation: Universality and efficiency. In: Margenstern, M., Rogozhin, Y. (eds.) MCU 2001. LNCS, vol. 2055, pp. 276–287. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  23. 23.
    Pan, L., Păun, G.: Spiking neural P systems with anti-spikes. Intern. J. Computers, Comm. Control 4(3), 273–282 (2009)Google Scholar
  24. 24.
    Pavel, A.B., Arsene, O., Buiu, C.: Enzymatic numerical P systems – a new class of membrane computing systems. In: The IEEE Fifth Intern. Conf. on Bio-Inspired Computing. Theory and applications. BIC-TA 2010, Liverpool, pp. 1331–1336 (September 2010)Google Scholar
  25. 25.
    Pavel, A.B., Vasile, C.I., Dumitrache, I.: Robot localization implemented with enzymatic numerical P systems. In: Prescott, T.J., Lepora, N.F., Mura, A., Verschure, P.F.M.J. (eds.) Living Machines 2012. LNCS, vol. 7375, pp. 204–215. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  26. 26.
    Păun, G.: Computing with membranes. J. Comput. Syst. Sci. 61, 108–143 (2000) (see also TUCS Report 208, November 1998, www.tucs.fi)Google Scholar
  27. 27.
    Păun, G: Computing with membranes – A variant. Intern. J. Found. Computer Sci. 11(1), 167–182 (2000)Google Scholar
  28. 28.
    Păun, G.: Membrane Computing. An Introduction. Springer, Berlin (2002)Google Scholar
  29. 29.
    Păun, G.: Spiking neural P systems with astrocyte-like control. JUCS 13(11), 1707–1721 (2007)Google Scholar
  30. 30.
    Păun, G.: Some open problems about numerical P systems. In: Proc. 11th Brainstorming Week on Membrane Computing, February 4-8, Fénix Editora, Sevilla (2013)Google Scholar
  31. 31.
    Păun, G., Păun, R.: Membrane computing and economics: Numerical P systems. Fundamenta Informaticae 73, 213–227 (2006)Google Scholar
  32. 32.
    Păun, G., Pérez-Jiménez, M.J.: Solving problems in a distributed way in membrane computing: dP systems. Int. J. of Computers, Communication and Control 5(2), 238–252 (2010)Google Scholar
  33. 33.
    Păun, G., Rozenberg, G., Salomaa, A. (eds.): The Oxford Handbook of Membrane Computing. Oxford University Press (2010)Google Scholar
  34. 34.
    Păun, G., Yu, S.: On synchronization in P systems. Fundamenta Informaticae 38(4), 397–410 (1999)Google Scholar
  35. 35.
    Song, T., Pan, L., Păun, G.: Spiking neural P systems with rules on synapses. Submitted (2013)Google Scholar
  36. 36.
    Sosí, P.: k: A catalytic P system with two catalysts generating a non-semilinear set. Romanian J. Inf. Sci. Technology (in press)Google Scholar
  37. 37.
    Sosík, P., Valík, O.: On evolutionary lineages of membrane systems. In: Freund, R., Păun, G., Rozenberg, G., Salomaa, A. (eds.) WMC 2005. LNCS, vol. 3850, pp. 67–78. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  38. 38.
    Syropoulos, A.: Hypercomputation: Computing Beyond the Church-Turing Barrier. Springer, Berlin (2008)CrossRefGoogle Scholar
  39. 39.
    Vasile, C.I., Pavel, A.B., Kelemen, J.: Implementing obstacle avoidance and follower behaviors on Koala robots using numerical P systems. In: Tenth Brainstorming Week on Membrane Computing, Sevilla, vol. II, pp. 215–227 (2012)Google Scholar
  40. 40.
    Vasile, C.I., Pavel, A.B., Dumitrache, I.: Universality of enzymatic numerical P systems. In: Intern. J. Computer Math (in press)Google Scholar
  41. 41.
    Vasile, C.I., Pavel, A.B., Dumitrache, I., Păun, G.: On the power of enzymatic numerical P systems. Acta Informatica 49(6), 395–412 (2012)CrossRefzbMATHMathSciNetGoogle Scholar
  42. 42.
    The P Systems Website, http://ppage.psystems.eu

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Gheorghe Păun
    • 1
    • 2
  1. 1.Institute of Mathematics of the Romanian AcademyBucureştiRomania
  2. 2.Department of Computer Science and Artificial IntelligenceUniversity of SevillaSevillaSpain

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