Characterizing Tractability by Tissue-Like P Systems
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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- 1.Díaz–Pernil, D.: Sistemas celulares de tejidos: Formalización y eficiencia computacional. Ph D. Thesis, University of Sevilla (2008)Google Scholar
- 2.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
- 3.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)Google Scholar
- 6.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)Google Scholar
- 11.Păun, Gh., Pérez–Jiménez, M.J.: Recent computing models inspired from biology: DNA and membrane computing. Theoria 18(46), 72–84 (2003)Google Scholar
- 12.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)Google Scholar
- 14.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)Google Scholar
- 15.P systems web page, http://ppage.psystems.eu/