Abstract
The usefulness of P systems with membrane creation for solving NP problems has been previously proved (see [2, 3]), but, up to now, it was an open problem whether such P systems were able to solve PSPACE-complete problems in polynomial time. In this paper we give an answer to this question by presenting a uniform family of P system with membrane creation which solves the QSAT-problem in linear time.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
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, M.A., Pérez-Jiménez, M.J., Romero-Campero, F.J.: A linear solution of Subset Sum Problem by using Mmmbrane creation. In: Mira, J., Álvarez, J.R. (eds.) IWINAC 2005. LNCS, vol. 3561, pp. 258–267. Springer, Heidelberg (2005)
Gutiérrez-Naranjo, M.A., Pérez-Jiménez, M.J., Romero-Campero, F.J.: Solving SAT with Membrane Creation. In: Barry Cooper, S., Lowe, B., Torenvliet, L. (eds.) Computability in Europe 2005, CiE 2005: New Computational Paradigms, Report ILLC X-2005-01, University of Amsterdam, pp. 82–91 (2005)
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)
Luisi, P.L.: The chemical implementation of autopoiesis. In: Fleishaker, G.R., et al. (eds.) Self-Production of Supramolecular Structures. Kluwer, Dordrecht (1994)
Papadimitriou, C.H.: Computational Complexity. Addison-Wesley, Reading (1994)
Păun, G.: Membrane Computing. An Introduction. Springer, Berlin (2002)
Păun, G., Pérez-Jiménez, M.J.: Recent computing models inspired from biology: DNA and membrane computing. Theoria 18(46), 72–84 (2003)
Păun, G.: Further open problems in membrane computing. In: Păun, G., Riscos-núñez, A., Romero-Jiménez, A., Sancho-Caparrini, F. (eds.) Proceedings of the Second Brainstorming Week on Membrane Computing, Report RGNC 01/04, University of Seville, pp. 354–365 (2004)
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 solution for the Knapsack problem using 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-Campero, F.J.: Solving the BIN PACKING problem by recognizer P systems with active membranes. In: Păun, G., Riscos-Núñez, A., Romero-Jiménez, A., Sancho-Caparrini, F. (eds.) Proceedings of the Second Brainstorming Week on Membrane Computing, Report RGNC 01/04, University of Seville, pp. 414–430 (2004)
Pérez-Jiménez, M.J., Romero-Jiménez, A., Sancho-Caparrini, F.: A polynomial complexity class in P systems using membrane division. In: Csuhaj-Varjú, E., Kintala, C., Wotschke, D., Vaszyl, G. (eds.) Proceedings of the 5th Workshop on Descriptional Complexity of Formal Systems, DCFS 2003, pp. 284–294 (2003)
Stockmeyer, L.J., Meyer, A.R.: Word problems requiring exponential time. In: Proc. 5th ACM Symp. on the Theory of Computing, pp. 1–9 (1973)
P systems web page, http://psystems.disco.unimib.it/
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Gutiérrez-Naranjo, M.A., Pérez-Jiménez, M.J., Romero-Campero, F.J. (2006). A Linear Solution for QSAT with Membrane Creation. In: Freund, R., Păun, G., Rozenberg, G., Salomaa, A. (eds) Membrane Computing. WMC 2005. Lecture Notes in Computer Science, vol 3850. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11603047_17
Download citation
DOI: https://doi.org/10.1007/11603047_17
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-30948-2
Online ISBN: 978-3-540-32340-2
eBook Packages: Computer ScienceComputer Science (R0)