Enzymatic Numerical P Systems Using Elementary Arithmetic Operations

  • Alberto Leporati
  • Giancarlo Mauri
  • Antonio E. Porreca
  • Claudio Zandron
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8340)


We prove that all-parallel enzymatic numerical P systems whose production functions can be expressed as a combination of sums, differences, products and integer divisions characterise PSPACE when working in polynomial time. We also show that, when only sums and differences are available, exactly the problems in P can be solved in polynomial time. These results are proved by showing how EN P systems and random access machines, running in polynomial time and using the same basic operations, can simulate each other efficiently.


Polynomial Time Production Function Arithmetic Operation Turing Machine Membrane Computing 
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  1. 1.
    Bertoni, A., Mauri, G., Sabadini, N.: A characterization of the class of functions computable in polynomial time on random access machines. In: STOC 1981 Proceedings of the Thirteenth Annual ACM Symposium on Theory of Computing, pp. 168–176 (1981),
  2. 2.
    Bottoni, P., Martin-Vide, C., Păun, G., Rozenberg, G.: Membrane systems with promoters/inhibitors. Acta Informatica 38(10), 695–720 (2002), CrossRefzbMATHMathSciNetGoogle Scholar
  3. 3.
    Buiu, C., Vasile, C., Arsene, O.: Development of membrane controllers for mobile robots. Information Sciences 187, 33–51 (2012), CrossRefGoogle Scholar
  4. 4.
    Cook, S.A., Reckhow, R.A.: Time bounded random access machines. Journal of Computer and System Sciences 7, 354–375 (1973), Google Scholar
  5. 5.
    Hartmanis, J., Simon, J.: On the power of multiplication in random access machines. In: IEEE Conference Record of 15th Annual Symposium on Switching and Automata Theory, pp. 13–23 (1974),
  6. 6.
    Leporati, A., Porreca, A.E., Zandron, C., Mauri, G.: Improved universality results for parallel enzymatic numerical P systems. International Journal of Unconventional Computing 9, 385–404 (2013), Google Scholar
  7. 7.
    Papadimitriou, C.H.: Computational Complexity. Addison-Wesley (1993)Google Scholar
  8. 8.
    Păun, G., Păun, R.: Membrane computing and economics: Numerical P systems. Fundamenta Informaticae 73(1-2), 213–227 (2006), zbMATHMathSciNetGoogle Scholar
  9. 9.
    Păun, G., Rozenberg, G., Salomaa, A. (eds.): The Oxford Handbook of Membrane Computing. Oxford University Press (2010)Google Scholar
  10. 10.
    Pavel, A.B., Arsene, O., Buiu, C.: Enzymatic numerical P systems – A new class of membrane computing systems. In: Li, K., Tang, Z., Li, R., Nagar, A.K., Thamburaj, R. (eds.) Proceedings 2010 IEEE Fifth International Conference on Bio-Inspired Computing: Theories and Applications (BIC-TA 2010), pp. 1331–1336 (2010),
  11. 11.
    Pavel, A.B., Buiu, C.: Using enzymatic numerical P systems for modeling mobile robot controllers. Natural Computing 11(3), 387–393 (2012), CrossRefzbMATHMathSciNetGoogle Scholar
  12. 12.
    Vasile, C.I., Pavel, A.B., Dumitrache, I., Păun, G.: On the power of enzymatic numerical P systems. Acta Informatica 49, 395–412 (2012), CrossRefzbMATHMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Alberto Leporati
    • 1
  • Giancarlo Mauri
    • 1
  • Antonio E. Porreca
    • 1
  • Claudio Zandron
    • 1
  1. 1.Dipartimento di Informatica, Sistemistica e ComunicazioneUniversità degli Studi di Milano-BicoccaMilanoItaly

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