Abstract
We introduce the new concept of toxic objects, objects that must not stay idle as otherwise the computation is abandoned without yielding a result. P systems of many kinds using toxic objects allow for smaller descriptional complexity, especially for smaller numbers of rules, as trap rules can be avoided. Besides presenting a number of tiny P systems generating or accepting non-semilinear sets of (vectors of) natural numbers with very small numbers of rules, we also improve the results for catalytic and purely catalytic P systems: \(14\) rules for generating a non-semilinear vector set and \(29\) rules for generating a non-semilinear number set are sufficient when allowing only the minimal number of two and three catalysts, respectively; moreover, with using toxic objects, these numbers can be reduced to \(11\) and \(17\). Yet only \(23\) rules – without using toxic objects – are needed if we allow for using more catalysts, i.e., five for catalytic P systems and seven catalysts for purely catalytic P systems.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Alhazov, A., Freund, R.: Asynchronous and Maximally Parallel Deterministic Controlled Non-cooperative P Systems Characterize NFIN and coNFIN. In: Csuhaj-Varjú, E., Gheorghe, M., Rozenberg, G., Salomaa, A., Vaszil, Gy. (eds.) CMC 2012. LNCS, vol. 7762, pp. 101–111. Springer, Heidelberg (2013)
Alhazov, A., Freund, R.: Small P Systems Defining Non-semilinear Sets. Automata, Computation, Universality. Springer (to appear)
Alhazov, A.: P Systems without Multiplicities of Symbol-Objects. Information Processing Letters 100(3), 124–129 (2006)
Alhazov, A., Freund, R., Păun, Gh.: Computational Completeness of P Systems with Active Membranes and Two Polarizations. In: Margenstern, M. (ed.) MCU 2004. LNCS, vol. 3354, pp. 82–92. Springer, Heidelberg (2005)
Alhazov, A., Freund, R., Riscos-Núñez, A.: One and Two Polarizations, Membrane Creation and Objects Complexity in P Systems. In: Seventh International Symposium on Symbolic and Numeric Algorithms for Scientific Computing, SYNASC 2005, 385–394. EEE Computer Society (2005)
Alhazov, A., Verlan, S.: Minimization Strategies for Maximally Parallel Multiset Rewriting Systems. Theoretical Computer Science 412(17), 1581–1591 (2011)
Beyreder, M., Freund, R.: Membrane Systems Using Noncooperative Rules with Unconditional Halting. In: Corne, D.W., Frisco, P., Păun, Gh., Rozenberg, G., Salomaa, A. (eds.) WMC 2008. LNCS, vol. 5391, pp. 129–136. Springer, Heidelberg (2009)
Dassow, J., Păun, Gh.: Regulated Rewriting in Formal Language Theory. Springer (1989)
Freund, R.: Special Variants of P Systems Inducing an Infinite Hierarchy with Respect to the Number of Membranes. Bulletin of the EATCS 75, 209–219 (2001)
Freund, R., Kari, L., Oswald, M., Sosík, P.: Computationally Universal P Systems without Priorities: Two Catalysts Are Sufficient. Theoretical Computer Science 330(2), 251–266 (2005)
Freund, R., Leporati, A., Mauri, G., Porreca, A.E., Verlan, S., Zandron, C.: Flattening in (Tissue) P Systems. In: Alhazov, A., Cojocaru, S., Gheorghe, M., Rogozhin, Yu., Rozenberg, G., Salomaa, A. (eds.) CMC 2013. LNCS, vol. 8340, pp. 173–188. Springer, Heidelberg (2014)
Freund, R., Oswald, M., Păun, Gh.: Catalytic and Purely Catalytic P Systems and P Automata: Control Mechanisms for Obtaining Computational Completeness. Fundamenta Informaticae 136, 59–84 (2015)
Ibarra, O.H., Woodworth, S.: On Symport/Antiport P Systems with a Small Number of Objects. International Journal of Computer Mathematics 83(7), 613–629 (2006)
Minsky, M.L.: Computation: Finite and Infinite Machines. Prentice Hall, Englewood Cliffs (1967)
Păun, Gh.: Computing with Membranes. Journal of Computer and System Sciences 61(1), 108–143 (2000) (and Turku Center for Computer Science-TUCS Report 208, November 1998, www.tucs.fi)
Păun, Gh.: Membrane Computing: An Introduction. Springer (2002)
Păun, Gh., Rozenberg, G., Salomaa, A.: The Oxford Handbook of Membrane Computing, pp. 118–143. Oxford University Press (2010)
Rozenberg, G., Salomaa, A.: The Mathematical Theory of L Systems. Academic Press, New York (1980)
Rozenberg, G., Salomaa, A. (eds.): Handbook of Formal Languages, 3 vol. Springer (1997)
Sburlan, D.: Further Results on P Systems with Promoters/Inhibitors. International Journal of Foundations of Computer Science 17(1), 205–221 (2006)
Sosík, P.: A Catalytic P System with Two Catalysts Generating a Non-Semilinear Set. Romanian Journal of Information Science and Technology 16(1), 3–9 (2013)
Sosík, P., Langer, M.: Improved Universality Proof for Catalytic P Systems and a Relation to Non-Semi-Linear Sets. In: Bensch, S., Freund, R., Otto, F. (eds.): Sixth Workshop on Non-Classical Models of Automata and Applications (NCMA 2014), books@ocg.at, Band 304, Wien, pp. 223–234 (2014)
The P systems webpage: http://ppage.psystems.eu
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this paper
Cite this paper
Alhazov, A., Freund, R. (2014). P Systems with Toxic Objects. In: Gheorghe, M., Rozenberg, G., Salomaa, A., Sosík, P., Zandron, C. (eds) Membrane Computing. CMC 2014. Lecture Notes in Computer Science(), vol 8961. Springer, Cham. https://doi.org/10.1007/978-3-319-14370-5_7
Download citation
DOI: https://doi.org/10.1007/978-3-319-14370-5_7
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-14369-9
Online ISBN: 978-3-319-14370-5
eBook Packages: Computer ScienceComputer Science (R0)