Abstract
In this paper, a computational complexity theory within the framework of Membrane Computing is introduced. Polynomial complexity classes associated with different models of cell-like and tissue-like membrane systems are defined and the most relevant results obtained so far are presented. Many attractive characterizations of P ≠ NP conjecture within the framework of a bio-inspired and non-conventional computing model are deduced.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Alhazov, A., Pérez–Jiménez, M.J.: Uniform solution of QSAT using polarizationless active membranes. In: Durand-Lose, J., Margenstern, M. (eds.) MCU 2007. LNCS, vol. 4664, pp. 122–133. Springer, Heidelberg (2007)
Alhazov, A., Freund, R., Păun, Gh.: P systems with active membranes and two polarizations. In: Păun, Gh., et al. (eds.) Proc. Second Brainstorming Week on Membrane Computing, Report RGNC 01/04, Sevilla, pp. 20–35 (2004)
Alhazov, A., Pan, L., Păun, G.: Trading polarizations for labels in P systems with active membranes. Acta Informaticae 41(2-3), 111–144 (2004)
Alhazov, A., Martín–Vide, C., Pan, L.: Solving graph problems by P systems with restricted elementary active membranes. In: Jonoska, N., Păun, Gh., Rozenberg, G. (eds.) Aspects of Molecular Computing. LNCS, vol. 2950, pp. 1–22. Springer, Heidelberg (2003)
Alhazov, A., Martín–Vide, C., Pan, L.: Solving a PSPACE–complete problem by recognizing P systems with restricted active membranes. Fundamenta Informaticae 58, 67–77 (2003)
Díaz–Pernil, D., Gutiérrez–Naranjo, M.A., 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)
Garey, M.R., Johnson, D.S.: Computers and Intractability. A Guide to the Theory of NP-completeness. W.H. Freeman and Company, New York (1979)
Gutiérrez-Naranjo, R., Pérez-Jiménez, M.J., Rius–Font, M.: Characterizing tractability by tissue–like P systems. In: Gutiérrez–Escudero, R., et al. (eds.) Proc. Seventh Brainstorming Week on Membrane Computing, Fénix Editora, Seville, pp. 169–180 (2009)
Gutiérrez-Naranjo, M.A., Pérez-Jiménez, M.J., Riscos-Núñez, A.: A fast P system for finding a balanced 2-partition. Soft Computing 9(9), 673–678 (2005)
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., et al. (eds.) Formal Models, Languages and Applications, pp. 137–154. World Scientific, Singapore (2006)
Krishna, S.N., Rama, R.: A variant of P systems with active membranes: Solving NP–complete problems. Romanian Journal of Information Science and Technology 2(4), 357–367 (1999)
Leporati, A., Ferretti, C., Mauri, G., Pérez–Jiménez, M.J., Zandron, C.: Complexity aspects of polarizationless membrane systems. Natural Computing, http://dx.doi.org/10.1007/s11047-008-9100-1
Murphy, N., Woods, D.: Active membrane systems without charges and using only symetric elementary division characterise P. In: Eleftherakis, G., Kefalas, P., Păun, G., Rozenberg, G., Salomaa, A. (eds.) WMC 2007. LNCS, vol. 4860, pp. 367–384. Springer, Heidelberg (2007)
Obtulowicz, A.: Deterministic P systems for solving SAT problem. Romanian Journal of Information Science and Technology 4(1-2), 551–558 (2001)
Pan, L., Alhazov, A., Ishdorj, T.-O.: Further remarks on P systems with active membranes, separation, merging, and release rules. In: Păun, Gh., et al. (eds.) Proc. Second Brainstorming Week on Membrane Computing, Report RGNC 01/04, Sevilla, pp. 316–324 (2004)
Pan, L., Ishdorj, T.-O.: P systems with active membranes and separation rules. Journal of Universal Computer Science 10(5), 630–649 (2004)
Pan, L., Pérez-Jiménez, M.J.: Computational complexity of tissue–like P systems with cell separation (submitted, 2009)
Păun, A.: On P systems with membrane division. In: Antoniou, I., et al. (eds.) Unconventional Models of Computation, pp. 187–201. Springer, London (2000)
Păun, Gh.: Computing with membranes. Journal of Computer and System Sciences 61(1), 108–143 (2000); Turku Center for CS-TUCS Report No. 208 (1998)
Păun, Gh.: Membrane Computing. An Introduction. Springer, Berlin (2002)
Păun, Gh.: P systems with active membranes: Attacking NP–complete problems. Journal of Automata, Languages and Combinatorics 6(1), 75–90 (2001)
Păun, Gh.: Computing with membranes. Attacking NP–complete problems. In: Antoniou, I., et al. (eds.) Unconventional Models of Computation, pp. 94–115. Springer, London (2000)
Păun, Gh.: Further twenty six open problems in membrane computing. In: Gutiérrez-Naranjo, M.A., et al. (eds.) Proc. Third Brainstorming Week on Membrane Computing, Report RGNC 01/04, Fénix Editora, Sevilla, pp. 249–262 (2005)
Pérez–Jiménez, M.J.: An approach to computational complexity in membrane computing. In: Mauri, G., Păun, G., Jesús Pérez-Jímenez, M., Rozenberg, G., Salomaa, A. (eds.) WMC 2004. LNCS, vol. 3365, pp. 85–109. Springer, Heidelberg (2005)
Pérez-Jiménez, M.J., Riscos-Núñez, A.: Solving the Subset-Sum problem by active membranes. New Generation Computing 23(4), 367–384 (2005)
Pérez-Jiménez, M.J., Riscos-Núñez, A.: A linear–time solution to the Knapsack problem using P systems with active membranes. In: Martín-Vide, C., Mauri, G., Păun, G., Rozenberg, G., Salomaa, A. (eds.) WMC 2003. LNCS, vol. 2933, pp. 250–268. Springer, Heidelberg (2004)
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 (2006); A preliminary version in Csuhaj-Varjú, E., et al. (eds.) Proc. Fifth International Workshop on Descriptional Complexity of Formal Systems, DCFS 2003, Budapest, Hungary, July 12-14, pp. 284–294 (2003)
Pérez-Jiménez, M.J., Romero–Campero, F.J.: Attacking the common algorithmic problem by recognizer P systems. In: Margenstern, M. (ed.) MCU 2004. LNCS, vol. 3354, pp. 304–315. Springer, Heidelberg (2005)
Pérez–Jiménez, M.J., Romero–Campero, F.J.: An efficient family of P systems for packing items into bins. Journal of Universal Computer Science 10(5), 650–670 (2004)
Pérez–Jiménez, M.J., Romero-Campero, F.J.: Trading polarizations for bi-stable catalysts in P systems with active membranes. In: Mauri, G., Păun, G., Jesús Pérez-Jímenez, M., Rozenberg, G., Salomaa, A. (eds.) WMC 2004. LNCS, vol. 3365, pp. 373–388. Springer, Heidelberg (2005)
Pérez–Jiménez, M.J., Romero–Jiménez, A., Sancho–Caparrini, F.: Complexity classes in cellular computing with membranes. Natural Computing 2(3), 265–285 (2003)
Porreca, A.E.: Computational Complexity Classes for Membrane Systems, Master Degree Thesis, Universita’ di Milano-Bicocca, Italy (2008)
Porreca, A.E., Mauri, G., Zandron, C.: Complexity classes for membrane systems. Informatique théorique et applications 40(2), 141–162 (2006)
Riscos–Núñez, A.: Cellular Programming: efficient resolution of NP–complete numerical problems. PhD. Thesis, University of Sevilla, Spain (2004)
Sosík, P., Rodríguez–Patón, A.: Membrane computing and complexity theory: A characterization of PSPACE. Journal of Computer and System Sciences 73, 137–152 (2007)
Sosík, P.: The computational power of cell division. Natural Computing 2(3), 287–298 (2003)
Woods, D., Murphy, N., Pérez-Jiménez, M.J., Riscos-Núñez, A.: Membrane dissolution and division in P. LNCS, vol. 5715, pp. 263–277. Springer, Heidelberg (2009)
Zandron, C., Ferretti, C., Mauri, G.: Solving NP–complete problems using P systems with active membranes. In: Antoniou, I., Calude, C.S., Dinneen, M.J. (eds.) Unconventional Models of Computation, pp. 289–301. Springer, Heidelberg (2000)
Zandron, C., Leporati, A., Ferretti, C., Mauri, G., Pérez–Jiménez, M.J.: On the computational efficiency of polarizationless recognizer P systems with strong division and dissolution. Fundamenta Informaticae 87(1), 79–91 (2008)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Pérez–Jiménez, M.J. (2010). A Computational Complexity Theory in Membrane Computing. 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_10
Download citation
DOI: https://doi.org/10.1007/978-3-642-11467-0_10
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-11466-3
Online ISBN: 978-3-642-11467-0
eBook Packages: Computer ScienceComputer Science (R0)