Abstract
Energy–based P systems have been recently introduced as P systems in which the amount of energy consumed and/or manipulated during computations is taken into account. In this paper we consider conservative computations performed by energy–based P systems, that is, computations for which the amount of energy entering the system is the same as the amount of energy leaving it. We show that conservative computations naturally allow to define an NP–hard optimization problem, here referred to as Min Storage, and a corresponding NP–complete decision problem, ConsComp. Finally, we present a polynomial time 2–approximation algorithm for Min Storage.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Alford, G.: Membrane Systems with Heat Control. In: Pre–Proceedings of the Workshop on Membrane Computing, Curtea de Arges, Romania (August 2002), Available at: http://psystems.disco.unimib.it/
Ausiello, G., Crescenzi, P., Gambosi, G., Kann, V., Marchetti–Spaccamela, A., Protasi, M.: Complexity and Approximation. Combinatorial Optimization Problems and Their Approximability Properties. Springer, Heidelberg (1999)
Castellanos, J., Păun, G., Rodriguez–Paton, A.: P Systems with Worm-Objects. In: IEEE 7th International Conference on String Processing and Information Retrieval, SPIRE 2000, La Coruna, Spain, pp. 64–74 (2000) See also CDMTCS Technical Report 123, University of Auckland (2000), Available at: http://www.cs.auckland.ac.nz/CDMTCS
Cattaneo, G., Della Vedova, G., Leporati, A., Leporini, R.: Towards a Theory of Conservative Computing. Accepted on International Journal of Theoretical Physics (November 2002)Preprint available at http://arxiv.org/abs/quant-ph/0211085
Freund, R.: Energy–Controlled P Systems. In: Păun, G., Rozenberg, G., Salomaa, A., Zandron, C. (eds.) WMC 2002. LNCS, vol. 2597, pp. 247–260. Springer, Heidelberg (2003)
Freund, R., Leporati, A., Oswald, M., Zandron, C.: Sequential P Systems with Unit Rules and Energy. In: Margenstern, M. (ed.) MCU 2004. To appear in LNCS, vol. 3354, pp. 200–210. Springer, Heidelberg (2005)
Frisco, P.: The Conformon–P Systems: A Molecular and Cell Biology–Inspired Computability Model. Theoretical Computer Science 312, 295–319 (2004)
Frisco, P., Ji, S.: Info–Energy P Systems. In: Proceedings of DNA 8, Eighth International Meeting on DNA Based Computers, Hokkaido University, Japan (June 2002)
Frisco, P., Ji, S.: Towards a Hierarchy of Conformons–P Systems. In: Păun, G., Rozenberg, G., Salomaa, A., Zandron, C. (eds.) WMC 2002. LNCS, vol. 2597, pp. 302–318. Springer, Heidelberg (2003)
Garey, M.R., Johnson, D.S.: Computers and Intractability. A Guide to the Theory on NP–Completeness. W. H. Freeman and Company, New York (1979)
Gens, G.V., Levner, E.V.: Computational Complexity of Approximation Algorithms for Combinatorial Problems. In: MFCS 1979. LNCS, vol. 74, pp. 292–300. Springer, Berlin (1979)
Ibarra, O.H., Kim, C.E.: Fast Approximation Algorithms for the Knapsack and Sum of Subset Problems. Journal of the ACM 22, 463–468 (1975)
Leporati, A., Zandron, C., Mauri, G.: Simulating the Fredkin Gate with Energy–based P Systems. In: [19], pp. 292–308
Leporati, A., Zandron, C., Mauri, G.: Universal families of Reversible P Systems. In: Margenstern, M. (ed.) MCU 2004. To appear in Lecture Notes in Computer Science, vol. 3354, pp. 257–268. Springer, Heidelberg (2005)
Mauri, G., Leporati, A.: On the Computational Complexity of Conservative Computing. In: Rovan, B., Vojtáš, P. (eds.) MFCS 2003. LNCS, vol. 2747, pp. 92–112. Springer, Heidelberg (2003)
Păun, G.: Computing with Membranes. Journal of Computer and System Sciences 1(61), 108–143 (2000), http://www.tucs.fi/Publications/techreports/TR208.php
Păun, G.: Computing with Membranes. An Introduction. Bulletin of the EATCS 67, 139–152 (1999)
Păun, G.: Membrane Computing. An Introduction. Springer, Berlin (2002)
Păun, G., Riscos Nuñez, A., Romero Jiménez, A., Sancho Caparrini, F.(eds.): In: Proceedings of Second Brainstorming Week on Membrane Computing, Seville, Spain, February 2–7 (2004); Department of Computer Sciences and Artificial Intelligence, University of Seville TR 01/2004
Păun, G., Rozenberg, G.: A Guide to Membrane Computing. Theoretical Computer Science 287(1), 73–100 (2002)
Păun, G., Suzuki, Y., Tanaka, H.: P Systems with Energy Accounting. International Journal Computer Math. 78(3), 343–364 (2001)
The P systems Web page: http://psystems.disco.unimib.it/
Vollmer, H.: Introduction to Circuit Complexity: A Uniform Approach. Springer, Heidelberg (1999)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Leporati, A., Zandron, C., Mauri, G. (2005). Conservative Computations in Energy–Based P Systems. In: Mauri, G., Păun, G., Pérez-Jiménez, M.J., Rozenberg, G., Salomaa, A. (eds) Membrane Computing. WMC 2004. Lecture Notes in Computer Science, vol 3365. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-31837-8_22
Download citation
DOI: https://doi.org/10.1007/978-3-540-31837-8_22
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-25080-7
Online ISBN: 978-3-540-31837-8
eBook Packages: Computer ScienceComputer Science (R0)