Abstract
Proton pumping P systems are a variant of membrane systems with both rewriting rules and symport/antiport rules, where a set of objects called protons is distinguished, every cooperative symport or antiport rule involves a proton, but no rewriting rule does. Time-freeness property means the result of all computations does not depend on the time it takes to execute the rules.
The goal of this article is to improve (showing that two membranes are sufficient) the known universality results on proton pumping P systems, establishing at the same time an upper bound on the number of protons, namely one, or four for time-free systems.
All results mentioned hold for proton pumping P systems with non-cooperative rewriting and either symport/antiport rules of weight one (classical variant) or symport rules of weight at most two. As a corollary, we obtain the universality of P systems with one membrane and one bi-stable catalyst, or the universality of time-free P systems with one membrane and four bi-stable catalysts. All universality results are stated as generating RE (except the time-free systems without targets generate PsRE).
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Alberts, B., et al.: Essential Cell Biology, An Introduction to the Molecular Biology of the Cell. Garland Publ., New York (1998)
Alhazov, A.: Minimizing evolution-communication P systems and automata. In: [8], pp. 23–31; New Generation Computing 22, 299–310 (2004)
Alhazov, A.: Number of protons/bi-stable catalysts and membranes in P systems. Time-freeness. In: Freund, R., Lojka, G., Oswald, M., Păun, G. (eds.) Preproceedings of the Workshop on Membrane Computing, Vienna Institute of Technology, pp. 102–122 (2005)
Alhazov, A., Cavaliere, M.: Evolution-communication P systems: Time-freeness. In: Gutiérrez-Naranjo, M.A., Riscos-Núñ ez, A., Romero-Campero, F.J., Sburlan, D. (eds.) Proceedings of the Third Brainstorming Week on Membrane Computing.Technical Report 01/2005, Sevilla University, pp. 11–18 (2005)
Alhazov, A., Cavaliere, M.: Proton pumping P systems. In: Alhazov, A., Martín-Vide, C., Păun, G. (eds.) Preproceedings of the Workshop on Membrane Computing. Technical Report 28/03, Rovira i Virgili University, Tarragona, pp. 1–16; In: Martín-Vide, C., Mauri, G., Păun, G., Rozenberg, G., Salomaa, A. (eds.) Membrane Computing, International Workshop, WMC, Tarragona, Revised Papers, LNCS 2933, pp. 1–18. Springer, Berlin (2003)
Cavaliere, M.: Evolution-communication P systems. In: Păun, G., Rozenberg, G., Salomaa, A., Zandron, C. (eds.) WMC 2002. LNCS, vol. 2597, pp. 134–145. Springer, Heidelberg (2003)
Cavaliere, M., Deufemia, V.: Further results on time-free P systems. In: Gutiérrez-Naranjo, M.A., Păun, G., Pérez-Jiménez, M.J. (eds.) Proceedings of the ESF PESC Exploratory Workshop on Cellular Computing (Complexity Aspects), pp. 95–116. Fénix Editora, Sevilla (2005)
Cavaliere, M., Martín-Vide, C., Păun, G. (eds.): Brainstorming Week on Membrane Computing. Technical Report 26/03, Rovira i Virgili University, Tarragona (2003)
Cavaliere, M., Sburlan, D.: Time-independent P systems. In: Mauri, G., Păun, G., Jesús Pérez-Jímenez, M., Rozenberg, G., Salomaa, A. (eds.) WMC 2004. LNCS, vol. 3365, pp. 239–258. Springer, Heidelberg (2005)
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)
Krishna, S.N., Păun, A.: Some universality results on evolution-communication P systems. In: [8], pp. 207–215; New Generation Computing 22, 377–394 (2004)
Krishna, S.N., Păun, A.: Three universality results on P systems. In: [8], pp. 198–206
Minsky, M.L.: Finite and Infinite Machines. Prentice Hall, Englewood Cliffs (1967)
Păun, G.: Computing with Membranes: An Introduction. Springer, Berlin (2002)
Saier Jr., M.H.: A functional-phylogenetic classification system for transmembrane solute transporters. Microbiology and Molecular Biology Reviews, 354–411 (2000)
The P systems Web Page: http://psystems.disco.unimib.it
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Alhazov, A. (2006). Number of Protons/Bi-stable Catalysts and Membranes in P Systems. Time-Freeness. In: Freund, R., Păun, G., Rozenberg, G., Salomaa, A. (eds) Membrane Computing. WMC 2005. Lecture Notes in Computer Science, vol 3850. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11603047_6
Download citation
DOI: https://doi.org/10.1007/11603047_6
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-30948-2
Online ISBN: 978-3-540-32340-2
eBook Packages: Computer ScienceComputer Science (R0)