Alhazov, Artiom; Belingheri, Omar; Freund, Rudolf; Ivanov, Sergiu; Porreca, Antonio E.; Zandron, Claudio Purely catalytic P systems over integers and their generative power. (English) Zbl 1483.68106 Leporati, Alberto (ed.) et al., Membrane computing. 17th international conference, CMC 2016, Milan, Italy, July 25–29, 2016. Revised selected papers. Cham: Springer. Lect. Notes Comput. Sci. 10105, 67-82 (2017). Summary: We further investigate the computing power of the recently introduced P systems with \(\mathbb Z\)-multisets (also known as hybrid sets) as generative devices. These systems apply catalytic rules in the maximally parallel way, even consuming absent non-catalysts, thus effectively generating vectors of arbitrary (not just non-negative) integers. The rules may only be made inapplicable by dissolution rules. However, this releases the catalysts into the immediately outer region, where new rules might become applicable to them. We discuss the generative power of this model. Finally, we consider the variant with mobile catalysts.For the entire collection see [Zbl 1358.68015]. MSC: 68Q07 Biologically inspired models of computation (DNA computing, membrane computing, etc.) PDFBibTeX XMLCite \textit{A. Alhazov} et al., Lect. Notes Comput. Sci. 10105, 67--82 (2017; Zbl 1483.68106) Full Text: DOI Link References: [1] Alhazov, A., Aman, B., Freund, R., Păun, G.: Matter and anti-matter in membrane systems. In: Jürgensen, H., Karhumäki, J., Okhotin, A. (eds.) DCFS 2014. LNCS, vol. 8614, pp. 65–76. Springer, Heidelberg (2014). doi: 10.1007/978-3-319-09704-6_7 · Zbl 1416.68067 [2] Alhazov, A., Belingheri, O., Freund, R., Ivanov, S., Porreca, A.E., Zandron, C.: Semilinear sets, register machines, and integer vector addition (P) systems. In: Leporati, A., Zandron, C. (eds.) Proceedings of the Seventeenth International Conference on Membrane Computing (CMC17), 25–29 July 2016, Milan, Italy, pp. 39–56. Università degli Studi di Milano-Bicocca (2016) [3] Belingheri, O., Porreca, A.E., Zandron, C.: P systems with hybrid sets. In: Gheorghe, M., Konur, S. (eds.) Proceedings of the Workshop on Membrane Computing WMC 2016, Manchester (UK), 11–15 July 2016. School of Electrical Engineering and Computer Science, University of Bradford, Bradford, BD7 1DP, UK. Technical Report UB-20160819-1, pp. 34–41. University of Bradford (2016) [4] Carette, J., Sexton, A.P., Sorge, V., Watt, S.M.: Symbolic domain decomposition. In: Autexier, S., Calmet, J., Delahaye, D., Ion, P.D.F., Rideau, L., Rioboo, R., Sexton, A.P. (eds.) CICM 2010. LNCS (LNAI), vol. 6167, pp. 172–188. Springer, Heidelberg (2010). doi: 10.1007/978-3-642-14128-7_16 · Zbl 1286.68515 [5] Freund, R., Ibarra, O., Păun, G., Yen, H.C.: Matrix languages, register machines, vector addition systems. In: Naranjo, M.A.G., Riscos-Núñez, A., Romero-Campero, F.J., Sburlan, D. (eds.) Third Brainstorming Week on Membrane Computing, pp. 155–167. Fénix Editora, Sevilla, España (2005) [6] Freund, R., Ivanov, S., Verlan, S.: P systems with generalized multisets over totally ordered abelian groups. In: Rozenberg, G., Salomaa, A., Sempere, J.M., Zandron, C. (eds.) CMC 2015. LNCS, vol. 9504, pp. 117–136. Springer, Heidelberg (2015). doi: 10.1007/978-3-319-28475-0_9 · Zbl 1473.68078 [7] Greibach, S.A.: Remarks on blind and partially blind one-way multicounter machines. Theoret. Comput. Sci. 7(3), 311–324 (1978) · Zbl 0389.68030 [8] Haase, C., Halfon, S.: Integer vector addition systems with states. In: Ouaknine, J., Potapov, I., Worrell, J. (eds.) RP 2014. LNCS, vol. 8762, pp. 112–124. Springer, Heidelberg (2014). doi: 10.1007/978-3-319-11439-2_9 · Zbl 1393.68115 [9] Hopcroft, J., Pansiot, J.J.: On the reachability problem for 5-dimensional vector addition systems. Theoret. Comput. Sci. 8(2), 135–159 (1979) · Zbl 0466.68048 [10] Krishna, S.N., Păun, A.: Results on catalytic and evolution-communication P systems. New Gener. Comput. 22(4), 377–394 (2004) · Zbl 1085.68051 [11] Păun, G.: Some quick research topics. http://www.gcn.us.es/files/OpenProblems_bwmc15.pdf [12] Păun, G.: Computing with membranes. J. Comput. Syst. Sci. 61, 108–143 (1998) · Zbl 0956.68055 [13] Păun, G., Rozenberg, G., Salomaa, A.: The Oxford Handbook of Membrane Computing. Oxford University Press Inc., New York (2010) · Zbl 1179.68004 [14] The P Systems Website: http://ppage.psystems.eu This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.