Eilenberg P Systems with Symbol-Objects

  • Francesco Bernardini
  • Marian Gheorghe
  • Mike Holcombe
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2950)


A class of P systems, called EOP systems, with symbol objects processed by evolution rules distributed alongside the transitions of an Eilenberg machine, is introduced. A parallel variant of EOP systems, called EOPP systems, is also defined and the power of both EOP and EOPP systems is investigated in relationship with three parameters: number of membranes, states and set of distributed rules. It is proven that the family of Parikh sets of vectors of numbers generated by EOP systems with one membrane, one state and one single set of rules coincides with the family of Parikh sets of context-free languages. The hierarchy collapses when at least one membrane, two states and four sets of rules are used and in this case a characterization of the family of Parikh sets of vectors associated with ET0L languages is obtained. It is also shown that every EOP system may be simulated by an EOPP system and EOPP systems may be used for solving NP-complete problems. In particular linear time solutions are provided for the SAT problem.


Conjunctive Normal Form Priority Relationship Evolution Rule Terminal Symbol Membrane Computing 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Bălănescu, T., Gheorghe, M., Holcombe, M., Ipate, F.: Eilenberg P systems. In: Păun, G., Rozenberg, G., Salomaa, A., Zandron, C. (eds.) WMC 2002. LNCS, vol. 2597, pp. 43–57. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  2. 2.
    Bălănescu, T., Cowling, T., Georgescu, H., Gheorghe, M., Holcombe, M., Vertan, C.: Communicating stream X-machines systems are no more than X-machines. J. Universal Comp. Sci. 5, 494–507 (1997)Google Scholar
  3. 3.
    Calude, C., Păun, G.: Computing with Cells and Atoms. Taylor and Francis, London (2000)Google Scholar
  4. 4.
    Csuhaj-Varju, E., Dassow, J., Kelemen, J., Păun, G.: Grammar Systems. Gordon & Breach, London (1994)zbMATHGoogle Scholar
  5. 5.
    Dassow, J., Păun, G.: Regulated Rewriting in Formal Language Theory. Springer, Berlin (1989)Google Scholar
  6. 6.
    Eilenberg, S.: Automata, Languages and Machines. Academic Press, New York (1974)zbMATHGoogle Scholar
  7. 7.
    Ferretti, C., Mauri, G., Păun, G., Zandron, C.: On three variants of rewriting P systems. In: Martin-Vide, C., Păun, G. (eds.) Pre-proceedings of Workshop on Membrane Computing (WMC-CdeA2001), Curtea de Argeş, Romania, August 2001, pp. 63–76 (2001), Theor. Comp. Sci. (to appear)Google Scholar
  8. 8.
    Gheorghe, M.: Generalised stream X-machines and cooperating grammar systems. Formal Aspects of Computing 12, 459–472 (2000)zbMATHCrossRefGoogle Scholar
  9. 9.
    Holcombe, M.: X-machines as a basis for dynamic system specification. Software Engineering Journal 3, 69–76 (1998)CrossRefGoogle Scholar
  10. 10.
    Holcombe, M., Ipate, F.: Correct Systems Building a Business Process Solution. Applied Computing Series. Springer, Berlin (1998)zbMATHGoogle Scholar
  11. 11.
    Krishna, S.N., Rama, R.: P systems with replicated rewriting. Journal of Automata, Languages and Combinatorics 6, 345–350 (2001)zbMATHMathSciNetGoogle Scholar
  12. 12.
    Păun, G.: Computing with membranes. Journal of Computer System Sciences 61, 108–143 (1998), and Turku Center for Computer Science, TUCS Report 208,
  13. 13.
    Păun, G.: Membrane computing. An Introduction. Springer, Berlin (2002)zbMATHGoogle Scholar
  14. 14.
    Rozenberg, G., Salomaa, A.: The Mathematical Theory of L Systems. Academic Press, New York (1980)zbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Francesco Bernardini
    • 1
  • Marian Gheorghe
    • 1
  • Mike Holcombe
    • 1
  1. 1.Department of Computer ScienceThe University of SheffieldRegent CourtUK

Personalised recommendations