Abstract
In the framework of recognizer cell–like membrane systems it is well known that the construction of exponential number of objects in polynomial time is not enough to efficiently solve NP–complete problems. Nonetheless, it may be sufficient to create an exponential number of membranes in polynomial time.
In this paper, we study the computational efficiency of recognizer tissue P systems with communication (symport/antiport) rules and division rules. Some results have been already obtained in this direction: (a) using communication rules and making no use of division rules, only tractable problems can be efficiently solved; (b) using communication rules with length three and division rules, NP–complete problems can be efficiently solved. In this paper, we show that the length of communication rules plays a relevant role from the efficiency point of view for this kind of P systems.
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Díaz–Pernil, D.: Sistemas celulares de tejidos: Formalización y eficiencia computacional. Ph D. Thesis, University of Sevilla (2008)
Díaz–Pernil, D., Pérez–Jiménez, M.J., Romero–Jiménez, A.: Efficient simulation of tissue-like P systems by transition cell-like P systems. Natural Computing, http://dx.doi.org/10.1007/s11047-008-9102-z
Díaz–Pernil, D., Pérez–Jiménez, M.J., Riscos–Núñez, A., Romero–Jiménez, A.: Computational efficiency of cellular division in tissue-like membrane systems. Romanian Journal of Information Science and Technology 11(3), 229–241 (2008)
Frisco, P., Hoogeboom, H.J.: Simulating counter automata by P systems with symport/antiport. In: Păun, G., Rozenberg, G., Salomaa, A., Zandron, C. (eds.) WMC 2002. LNCS, vol. 2597, pp. 288–301. Springer, Heidelberg (2003)
Gutiérrez–Naranjo, M.A., Pérez–Jiménez, M.J., Riscos–Núñez, A., Romero–Campero, F.J.: On the power of dissolution in P systems with active membranes. In: Freund, R., Păun, G., Rozenberg, G., Salomaa, A. (eds.) WMC 2005. LNCS, vol. 3850, pp. 224–240. Springer, Heidelberg (2006)
Gutiérrez–Naranjo, M.A., Pérez–Jiménez, M.J., Riscos–Núñez, A., Romero–Campero, F.J., Romero–Jiménez, A.: Characterizing tractability by cell-like membrane systems. In: Subramanian, K.G., Rangarajan, K., Mukund, M. (eds.) Formal models, languages and applications, ch. 9, pp. 137–154. World Scientific, Singapore (2006)
Martín–Vide, C., Pazos, J., Păun, Gh., Rodríguez–Patón, A.: Tissue P systems. Theoretical Computer Science 296, 295–326 (2003)
Păun, A., Păun, Gh.: The power of communication: P systems with symport/antiport. New Generation Computing 20(3), 295–305 (2002)
Păun, Gh.: Computing with membranes. Journal of Computer and System Sciences 61(1), 108–143 (2000)
Păun, Gh.: Membrane Computing. An Introduction. Springer, Berlin (2002)
Păun, Gh., Pérez–Jiménez, M.J.: Recent computing models inspired from biology: DNA and membrane computing. Theoria 18(46), 72–84 (2003)
Păun, Gh., Pérez–Jiménez, M.J., Riscos–Núñez, A.: Tissue P Systems with cell division. International Journal of Computers, Communications & Control III(3), 295–303 (2008); A preliminary version in Păun, Gh., et al. (eds.) Second Brainstorming Week on Membrane Computing, Sevilla, Report RGNC 01/2004, pp. 380–386 (2004)
Pérez–Jiménez, M.J., Romero–Jiménez, A., Sancho–Caparrini, F.: Complexity classes in cellular computing with membranes. Natural Computing 2(3), 265–285 (2003)
Pérez–Jiménez, M.J., Romero–Jiménez, A., Sancho–Caparrini, F.: A polynomial complexity class in P systems using membrane division. Journal of Automata, Languages and Combinatorics 11(4), 423–434 (2003); A preliminary version in Csuhaj-Varjú, E., et al. (eds.) Proc. Fifth Intern. Workshop on Descriptional Complexity of Formal Systems, DCFS 2003, Budapest, Hungary, July 12-14, 284–294 (2003)
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Gutiérrez–Escudero, R., Pérez–Jiménez, M.J., Rius–Font, M. (2010). Characterizing Tractability by Tissue-Like P Systems. In: Păun, G., Pérez-Jiménez, M.J., Riscos-Núñez, A., Rozenberg, G., Salomaa, A. (eds) Membrane Computing. WMC 2009. Lecture Notes in Computer Science, vol 5957. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11467-0_21
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DOI: https://doi.org/10.1007/978-3-642-11467-0_21
Publisher Name: Springer, Berlin, Heidelberg
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