Abstract
Catalytic P systems is one of the basic classes of P systems. The number of catalysts required for optimal universality results (both in pure catalytic systems and catalytic systems) has been a problem of extensive research [3],[5],[6],[7],[12]. The differences that can give universality/non-universality are very small in these systems, and finding this borderline is one of the ‘jewel’ problems in P systems [12]. In this paper, we try to figure out this borderline and have obtained some interesting results. We have proved that with 2 catalysts, if λ-rules are not used, then universality cannot be obtained. We also consider two restricted variants of pure catalytic systems and prove that they are also not universal. Finally, we look at mobile catalytic systems and solve two open problems.
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References
Dassow, J., Păun, Gh.: Regulated Rewriting in Formal Language Theory. Springer, Berlin (1989)
Dassow J.: Grammars with Regulated Rewriting, Handout given during the Ph.D school at Terragona (2003), theo.cs.uni-magdeburg.de/dassow/tarraphd.pdf
Freund, R., Kari, L., Oswald, M., Sosik, P.: Computationally universal P systems without priorities: two catalysts are sufficient. Theoretical Computer Science 330, 251–266 (2005)
Freund, R., Oswald, M., Sosik, P.: Reducing the number of catalysts required in computationally universal systems without priorities. In: Proceedings of DCFS 2003, pp. 102–113 (2003)
H. Ibarra, O., Yen, H.-C.: On Deterministic Catalytic Systems. In: Farré, J., Litovsky, I., Schmitz, S. (eds.) CIAA 2005. LNCS, vol. 3845, pp. 163–175. Springer, Heidelberg (2006)
H. Ibarra, O., Dang, Z., Egecioglu, O., Saxena, G.: Characterizations of Catalytic Membrane Computing Systems. In: Rovan, B., Vojtáš, P. (eds.) MFCS 2003. LNCS, vol. 2747, pp. 480–489. Springer, Heidelberg (2003)
Krishna, S.N., Păun, A.: Results on catalytic and evolution-communication P systems. New Generation Computing (22)4, 377–394 (2004)
Krishna, S.N.: On Pure Catalytic P Systems. Technical Report, IIT Bombay (2006), www.cse.iitb.ac.in/~krishnas/uc06.ps
Minsky, M.L.: Computation: Finite and Infinite Machines. Prentice-Hall, Englewood Cliffs (1967)
Papadimitriou, C.: Computational Complexity, 1st edn. Addison-Wesley, Reading (1993)
Păun, Gh.: Membrane Computing – An Introduction. Springer, Berlin (2002)
Păun, Gh.: 2006 Research Topics in Membrane Computing (manuscript, 2006)
Rozenberg, G., Salomaa, A. (eds.): Handbook of Formal Languages. Springer, Heidelberg (1997)
Sosik, P.: The power of catalysts and priorities in membrane computing. Grammars 6(1), 13–24 (2003)
Sosik, P., Freund, R.: P Systems without Priorities Are Computationally Universal. In: Păun, G., Rozenberg, G., Salomaa, A., Zandron, C. (eds.) WMC 2002. LNCS, vol. 2597, pp. 400–409. Springer, Heidelberg (2003)
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Krishna, S.N. (2006). On Pure Catalytic P Systems. In: Calude, C.S., Dinneen, M.J., Păun, G., Rozenberg, G., Stepney, S. (eds) Unconventional Computation. UC 2006. Lecture Notes in Computer Science, vol 4135. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11839132_13
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DOI: https://doi.org/10.1007/11839132_13
Publisher Name: Springer, Berlin, Heidelberg
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