Abstract
Objects generated in P systems usually are assumed to survive as long as the computation goes on. In this paper, decaying objects are considered, i.e., objects only surviving a bounded number of computation steps. Variants of (tissue) P systems with decaying objects working in transition modes where the number of rules applied in each computation step is bounded, are shown to be very restricted in their generative power, i.e., if the results are collected in a specified output cell/membrane, then only finite sets of multisets can be generated, and if the results are specified by the objects sent out into the environment, we obtain the regular sets. Only if the decaying objects are regenerated within a certain period of computation steps, i.e., if we allow an unbounded number of rules to be applied, then computational completeness can be obtained, yet eventually more ingredients are needed for the rules than in the case of non-decaying objects, e.g., permitting and/or forbidden contexts. As special variants of P systems, catalytic P systems, P systems using cooperative rules, and spiking neural P systems are investigated.
Access provided by Autonomous University of Puebla. Download to read the full chapter text
Chapter PDF
Similar content being viewed by others
Keywords
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.
References
Alhazov, A., Freund, R., Oswald, M., Slavkovik, M.: Extended Spiking Neural P Systems. In: Hoogeboom, H.J., Păun, G., Rozenberg, G., Salomaa, A. (eds.) WMC 2006. LNCS, vol. 4361, pp. 123–134. Springer, Heidelberg (2006)
Bernardini, F., Gheorghe, M., Margenstern, M., Verlan, S.: Networks of cells and Petri nets. In: Gutiérrez-Naranjo, M.A., Păun, G., Romero-Jiménez, A., Riscos-Núñez, A. (eds.) Proc. Fifth Brainstorming Week on Membrane Computing, Sevilla, pp. 33–62 (2007)
Brijder, R., Ehrenfeucht, A., Main, M.G., Rozenberg, G.: A tour of reaction systems. Int. J. Found. Comput. Sci. 22(7), 1499–1517 (2011)
Csuhaj-Varjú, E.: Networks of language processors, pp. 771–790 (2001)
Dassow, J., Păun, G.: Regulated Rewriting in Formal Language Theory. Springer (1989)
Dassow, J., Păun, G.: On the power of membrane computing. Journal of Universal Computer Science 5(2), 33–49 (1999)
Freund, R.: Transition and Halting Modes in (Tissue) P Systems. In: Păun, G., Pérez-Jiménez, M.J., Riscos-Núñez, A., Rozenberg, G., Salomaa, A. (eds.) WMC 2009. LNCS, vol. 5957, pp. 18–29. Springer, Heidelberg (2010)
Freund, R., Ionescu, M., Oswald, M.: Extended spiking neural P systems with decaying spikes and/or total spiking. Int. J. Found. Comput. Sci. 19(5), 1223–1234 (2008)
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)
Freund, R., Verlan, S.: A Formal Framework for Static (Tissue) P Systems. In: Eleftherakis, G., Kefalas, P., Păun, G., Rozenberg, G., Salomaa, A. (eds.) WMC 2007. LNCS, vol. 4860, pp. 271–284. Springer, Heidelberg (2007)
Freund, R., Verlan, S.: (Tissue) P systems working in the k-restricted minimally or maximally parallel transition mode. Natural Computing 10(2), 821–833 (2011)
Ionescu, M., Păun, G., Yokomori, T.: Spiking neural P systems. Fundamenta Informaticae 71(2-3), 279–308 (2006)
Kudlek, M., Martín-Vide, C., Păun, G.: Toward a Formal Macroset Theory. In: Calude, C.S., Pun, G., Rozenberg, G., Salomaa, A. (eds.) Multiset Processing. LNCS, vol. 2235, pp. 123–134. Springer, Heidelberg (2001)
Margenstern, M., Rogozhin, Y., Verlan, S.: Time-varying Distributed H Systems with Parallel Computations: the Problem is Solved. In: Chen, J., Reif, J.H. (eds.) DNA9. LNCS, vol. 2943, pp. 48–53. Springer, Heidelberg (2004)
Minsky, M.L.: Computation: Finite and Infinite Machines. Prentice Hall, Englewood Cliffs (1967)
Păun, G.: Computing with membranes. J. of Computer and System Sciences 61(1), 108–143 (1998); and TUCS Research Report 208 (1998), http://www.tucs.fi
Păun, G.: Membrane Computing. An Introduction. Springer, Berlin (2002)
Păun, G., Rozenberg, G., Salomaa, A.: The Oxford Handbook of Membrane Computing. Oxford University Press (2010)
Rozenberg, G., Salomaa, A.: Handbook of Formal Languages, vol. 3. Springer, Heidelberg (1997)
The P Systems Web Page, http://ppage.psystems.eu
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Freund, R. (2013). (Tissue) P Systems with Decaying Objects. In: Csuhaj-Varjú, E., Gheorghe, M., Rozenberg, G., Salomaa, A., Vaszil, G. (eds) Membrane Computing. CMC 2012. Lecture Notes in Computer Science, vol 7762. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-36751-9_1
Download citation
DOI: https://doi.org/10.1007/978-3-642-36751-9_1
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-36750-2
Online ISBN: 978-3-642-36751-9
eBook Packages: Computer ScienceComputer Science (R0)