Abstract
In this chapter we present a general framework to provide efficient solutions to decision problems through families of cell-like membrane systems constructed in a semi-uniform way (associating with each instance of the problem one P system solving it) or a uniform way (all instances of a decision problem having the same size are processed by the same system). We also show a brief compendium of efficient semi-uniform and uniform solutions to hard problems in these systems, and we explicitly describe some of these solutions.
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
A. Alhazov: P Systems with Active Membranes and Two Polarizations. In A. Riscos-Núñez, A. Romero-Jiménez, F. Sancho-Caparrini, eds.: Proceedings of the Second Brainstorming Week on Membrane Computing, Sevilla, February 2004, Report RGNC 01/04, Univ. of Sevilla, 2004 [27], 20–35.
A. Alhazov, T.-O. Ishdorj: Membrane Operations in P Systems with Active Membranes. In A. Riscos-Núñez, A. Romero-Jiménez, F. Sancho-Caparrini, eds.: Proceedings of the Second Brainstorming Week on Membrane Computing, Sevilla, February 2004, Report RGNC 01/04, Univ. of Sevilla, 2004 [27], 37–52.
A. Alhazov, C. Martín-Vide, L. Pan: Solving Graph Problems by P Systems with Restricted Elementary Active Membranes. In Aspects of Molecular Computing (N. Jonoska, Gh. Păun, G. Rozenberg, eds.), LNCS 2950, Springer, Berlin, 2004, 1–22.
J. Castellanos, Gh. Păun, A. Rodríguez-Patón: P Systems with Worm-Objects. IEEE 7th International Conference on String Processing and Information Retrieval, SPIRE 2000, La Coruña, Spain, 64–74.
A. Cordón-Franco, M.A. Gutiérrez-Naranjo, M.J. Pérez-Jiménez, F. Sancho-Caparrini: Implementing in Prolog an Effective Cellular Solution for the Knapsack Problem. In Gh. Păun, G. Rozenberg, A. Salomaa, eds.: Membrane Computing. International Workshop WMC2004, Tarragona, Spain, July 2003, Revised Papers. LNCS 2933, Springer, Berlin, 2004 [14] 140–152.
E. Czeizler: Self-Activating P Systems. In Membrane Computing. International Workshop WMC-CdeA 2002, Curtea de Argeş, Romania, August 2002, Revised Papers (Gh. Păun, G. Rozenberg, A, Salomaa, C. Zandron, eds.), LNCS 2597, Springer, Berlin, 2003, 234–246.
M.A. Gutiérrez-Naranjo, M.J. Pérez-Jiménez, A. Riscos-Núñez: A Fast P System for Finding a Balanced 2-Partition. Soft Computing, 9,7 (2005).
T. Head, M. Yamamura, S. Gal: Aqueous Computing: Writing on Molecules. Proceedings of the Congress on Evolutionary Computation 1999, IEEE Service Center, Piscataway, NJ, 1999, 1006–1010.
M. Ito, C. Martín-Vide, Gh. Păun: Characterization of Parikh Sets of ET0L Languages in Terms of P Systems. In Words, Semigroups, and Transducers (M. Ito, Gh. Păun, S. Yu, eds.), World Scientific, Singapore, 2001, 239–254.
S.N. Krishna, R. Rama: A Variant of P Systems with Active Membranes: Solving NP-Complete Problems. Romanian Journal of Information Science and Technology, 2,4 (1999), 357–367.
S.N. Krishna, R. Rama: P Systems with Replicated Rewriting. Journal of Automata, Languages and Combinatorics, 6,1 (2001), 345–350.
S.N. Krishna, R. Rama: Breaking DES Using P Systems. Theoretical Computer Science, 299,1–3 (2003), 495–508.
M. Madhu, K. Kristhivasan: P Systems with Membrane Creation: Universality and Efficiency. In Proceedings of Third International Conference on Universal, Machines and Computations, Chişinău, Moldova, 2001 (M. Margenstern, Y. Rogozhin, eds.), LNCS 2055, Springer, Berlin, 2001, 276–287.
C. Martí-Vide, Gh. Păun, G. Rozenberg, A. Salomaa, eds.: Membrane Computing. International Workshop WMC2004, Tarragona, Spain, July 2003, Revised Papers. LNCS 2933, Springer, Berlin, 2004
A. Obtulowicz: Deterministic P Systems for Solving SAT Problem. Romanian Journal of Information Science and Technology, 4,1–2 (2001), 551–558.
A. Obtulowicz: On P Systems with Active Membranes: Solving the Integer Factorization Problem in a Polynomial Time. In Multiset Processing. Mathematical, Computer Science, and Molecular Computing Points of View (C.S. Calude, Gh. Păun, G. Rozenberg, A. Salomaa, eds.), LNCS 2235, Springer, Berlin, 2001, 267–285.
A. Obtulowicz: Note on Some Recursive Family of P Systems with Active Membranes. Submitted, 2004.
L. Pan, A. Alhazov, T.-O. Ishdorj: Further Remarks on P Systems with Active Membranes, Separation, Merging, and Release Rules. In A. Riscos-Núñez, A. Romero-Jiménez, F. Sancho-Caparrini, eds.: Proceedings of the Second Brainstorming Week on Membrane Computing, Sevilla, February 2004, Report RGNC 01/04, Univ. of Sevilla, 2004 [27], 316–324.
L. Pan, T.-O. Ishdorj: P Systems with Active Membranes and Separation Rules. Journal of Universal Computer Science, 10,5 (2004), 630–649.
L. Pan, C. Martín-Vide: Solving Multiset 0–1 Knapsack Problem by P Systems with Input and Active Membranes. In A. Riscos-Núñez, A. Romero-Jiménez, F. Sancho-Caparrini, eds.: Proceedings of the Second Brainstorming Week on Membrane Computing, Sevilla, February 2004, Report RGNC 01/04, Univ. of Sevilla, 2004 [27], 342–353.
A. Păun: On P Systems with Membrane Division. In Unconventional Models of Computation (I. Antoniou, C.S. Calude, M.J. Dinneen, eds.), Springer, London, 2000, 187–201.
Gh. Păun: Computing with Membranes. Journal of Computer and System Sciences, 61,1 (2000), 108–143, and Turku Center for Computer Science-TUCS Report Nr. 208, 1998.
Gh. Păun: Computing with Membranes: Attacking NP-Complete Problems. In Unconventional Models of Computation (I. Antoniou, C.S. Calude, M.J. Dinneen, eds.), Springer, London, 2000, 94–115.
Gh. Păun: P systems with Active Membranes: Attacking NP-Complete Problems. Journal of Automata, Languages and Combinatorics, 6,1 (2001), 75–90.
Gh. Păun: Membrane Computing. An Introduction. Springer, Berlin, 2002.
Gh. Păun, M.J. Pérez-Jiménez, A. Riscos-Núñez: P Systems with Tables of Rules. In Theory is Forever, Essays Dedicated to Arto Salomaa on the Ocassion of His 70th Birthday (J. Karhumaki, H. Maurer, Gh. Păun, G. Rozenberg, eds.), LNCS 3113, Springer, Berlin, 2004, 235–249.
Gh. Păun, A. Riscos-Núñez, A. Romero-Jiménez, F. Sancho-Caparrini, eds.: Proceedings of the Second Brainstorming Week on Membrane Computing, Sevilla, February 2004, Report RGNC 01/04, Univ. of Sevilla, 2004.
Gh. Păun, G. Rozenberg: A Guide to Membrane Computing. Theoretical Computer Science, 287 (2002), 73–100.
Gh. Păun, Y. Suzuki, H. Tanaka, T. Yokomori: On the Power of Membrane Division in P Systems. Theoretical Computer Science, 324,1 (2004), 61–85.
M.J. Pérez-Jiménez, A. Riscos-Núñez: A Linear Time Solution to the Knapsack Problem Using Active Membranes. In Gh. Păun, G. Rozenberg, A. Salomaa, eds.: Membrane Computing. International Workshop WMC2004, Tarragona, Spain, July 2003, Revised Papers. LNCS 2933, Springer, Berlin, 2004 [14], 250–268.
M.J. Pérez-Jiménez, A. Riscos-Núñez: Solving the Subset-Sum Problem by P Systems with Active Membranes. New Generation Computing, in press.
M.J. Pérez-Jiménez, F.J. Romero-Campero: An Efficient Family of P Systems for Packing Items Into Bins. Journal of Universal Computer Science, 10,5 (2004), 650–670.
M.J. Pérez-Jiménez, F.J. Romero-Campero: Attacking the Common Algorithmic Problem by Recognizer P Systems. In Pre-proceedings of the Machines, Computations and Universality, MCU’2004 (abstracts), September 21–26, 2004, Sankt Petesburg, p. 27.
M.J. Pérez-Jiménez, A. Romero-Jiménez, F. Sancho-Caparrini: Teorí de la Complejidad en Modelos de Computación con Membranas. Ed. Kronos, Sevilla, 2002.
M.J. Pérez-Jiménez, A. Romero-Jiménez, F. Sancho-Caparrini: Complexity Classes in Models of Cellular Computing with Membranes. Natural Computing, 2,3 (2003), 265–285.
M.J. Pérez-Jiménez, A. Romero-Jiménez, F. Sancho-Caparrini: Solving VALIDITY Problem by Active Membranes with Input. In Proceedings of the Brainstorming Week on Membrane Computing, Tarragona, February 2003 (M. Cavaliere, C. Martín-Vide, Gh. Păun, eds.) Report GRLMC 26/03, 2003, 279–290.
A. Romero-Jiménez: Complexity and Universality in Cellular Computing Models. PhD. Thesis, University of Seville, Spain, 2003.
A. Romero-Jiménez, M.J. Pérez-Jiménez: Simulating Turing Machines by P Systems with External Output. Fundamenta Informaticae, 49,1–3 (2002), 273–287.
P. Sosik: The Computational Power of Cell Division. Natural Computing, 2,3 (2003), 287–298.
C. Zandron, C. Ferreti, G. Mauri: Solving NP-Complete Problems Using P Systems with Active Membranes. In Unconventional Models of Computation, UMC’2K (I. Antoniou, C.S. Calude, M.J. Dinneen, eds.), Springer, London, 2000, 289–301.
C. Zandron, G. Mauri, C. Ferreti, Universality and Normal Forms on Membrane Systems. In Proceedings of International Workshop on Grammar Systems, 2000 (R. Freund, A. Kelemenova, eds.), Bad Ischl, Austria, July 2000, 61–74.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Pérez-Jiménez, M.J., Romero-Jiménez, A., Sancho-Caparrini, F. (2006). Computationally Hard Problems Addressed Through P Systems. In: Ciobanu, G., Păun, G., Pérez-Jiménez, M.J. (eds) Applications of Membrane Computing. Natural Computing Series. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-29937-8_12
Download citation
DOI: https://doi.org/10.1007/3-540-29937-8_12
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-25017-3
Online ISBN: 978-3-540-29937-0
eBook Packages: Computer ScienceComputer Science (R0)