Skip to main content
SpringerLink
Log in

On the verification of membrane systems with dynamic structure

  • Published:
Natural Computing Aims and scope Submit manuscript

Abstract

We study computational properties of Gheorge Păun’s P-systems extended with rules that model in an abstract way creation, dissolution, fusion and cloning of membranes. We investigate decision problems like reachability of a configuration, boundedness (finiteness of the state space), and coverability (verification of safety properties). Our analysis is aimed at understanding the expressive power of rules that dynamically modify the structure of a membrane.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

Notes

  1. We consider here a slight generalization of the model in Dal Zilio and Formenti (2004) in which we allow any kind of transformation between two membranes.

  2. Notice that the intersection of upward-closed sets is always an upward-closed set.

References

  • Abdulla PA, Čerāns K, Jonsson B, Yih-Kuen T (1996) General decidability theorems for infinite-state systems. In: Proceedings of the 11th annual IEEE symposium on logic in computer science, LICS ’96, New Brunswick, New Jersey, 27–30 July 1996. IEEE Computer Society Press, Westbury, pp 313–321

  • Alhazov A, Freund R, Riscos-Núñez A (2006) Membrane division, restricted membrane creation and object complexity in P systems. Comput Math 83(7):529–547

    MATH  MathSciNet  Google Scholar 

  • Bernardini F, Manca V (2003) P systems with boundary rules. In: Proceedings of the international workshop on membrane computing, WMC ’03, Curtea de Arges, Romania, August 19–23, 2002, Lecture notes in computer science 2597. Springer, Berlin, pp 107–118

  • Besozzi D, Zandron C, Mauri G, Sabadini N (2001) P systems with gemmation of mobile membranes. In: Proceedings of the 7th Italian conference on theoretical computer science, ICTCS ’01, Torino, Italy, October 4–6, 2001. Lecture notes in computer science 2202. Springer, Berlin, pp 136–153

  • Besozzi D, Mauri G, Păun G, Zandron C (2003) Gemmating P systems: collapsing hierarchies. Theor Comput Sci 296(2):253–267

    Article  MATH  Google Scholar 

  • Bezem M, Klop JW, de Vrijer R (2003) Term rewriting systems. Cambridge University Press, Cambridge

    MATH  Google Scholar 

  • Dal Zilio S, Formenti E (2004) On the dynamics of PB systems: a Petri net view. In: Proceedings of the international workshop on membrane computing, WMC 2003, Tarragona, Spain, July 17–22, 2003, Revised Papers. Lecture notes in computer science 2933. Springer, Berlin, pp 153–167

  • Delzanno G, Montagna R (2007) On reachability and spatial reachability in fragments of bioambients. Electron Notes Theor Comput Sci 171(2):69–79

    Article  Google Scholar 

  • Delzanno G, Van Begin L (2007) On the dynamics of PB systems with volatile membranes. In: Proceedings of the International Workshop on Membrane Computing, WMC 2007, Tarragona, Spain, July 17–22, 2007. Lecture notes in computer science 4860. Springer, Berlin, pp 240–256

  • Delzanno G, Van Begin L (2008) A Biologically inspired model with fusion and clonation of membranes. In: Proceedings of the 7th international conference on unconventional computing, UC ’08, Vienna, Austria, August 25–28, 2008. Lecture notes in computer science 5204. Springer, Berlin, pp 64–82

  • Dickson LE (1913) Finiteness of the odd perfect and primitive abundant numbers with distinct factors. Am J Math 35:413–422

    Article  MATH  Google Scholar 

  • Finkel A, Schnoebelen Ph (2001) Well-structured transition systems everywhere! Theor Comput Sci 256(1–2):63–92

    Article  MATH  MathSciNet  Google Scholar 

  • Franco G, Manca V (2004) A membrane system for the leukocyte selective recruitment. In: Proceedings of the international workshop on membrane computing, WMC ’03, Tarragona, Spain, July 17–22, 2003. Lecture notes in computer science 2933. Springer, Berlin, pp 181–190

  • Ibarra OH, Dang Z, Egecioglu Ö (2004) Catalytic P systems, semilinear sets, and vector addition systems. Theor Comput Sci 312(2-3):379–399

    Article  MATH  MathSciNet  Google Scholar 

  • Kosaraju SR (1982) Decidability of reachability in vector addition systems. In: Proceedings of the 14th annual ACM symposium on theory of computing, STOC ’82, May 5–7, 1982. ACM, San Francisco, CA, pp 267–281

  • Kruskal JB (1960) Well-quasi ordering, the tree theorem, and Vazsonyi’s conjecture. Trans Am Math Soc 95:210–225

    MATH  MathSciNet  Google Scholar 

  • Li C, Dang Z, Ibarra OH, Yen H-C (2005) Signaling P systems and verification problems. In: Proceedings of the 32nd international colloquium on automata, languages and programming, ICALP ’05. Lisbon, Portugal, July 11–15, 2005. Lecture notes in computer science 3580. Springer, Berlin, pp 1462–1473

  • Mayr EW (1984) An algorithm for the general Petri net reachability problem. SIAM J Comput 13(3):441–460

    Article  MATH  MathSciNet  Google Scholar 

  • Minsky M (1967) Computation: finite and infinite machines. Prentice-Hall, Englewood Cliffs

    MATH  Google Scholar 

  • Păun Gh (2000) Computing with membranes. J Comput Syst Sci 61(1):108–143

    Article  MATH  Google Scholar 

  • Păun Gh (2001) P systems with active membranes: attacking NP-complete problems. J Autom Lang Comb 6(1):75–90

    MATH  MathSciNet  Google Scholar 

  • Păun A, Popa B (2006) P systems with proteins on membranes. Fundam Inform 72(4):467–483

    MATH  Google Scholar 

  • Păun Gh, Suzuki Y, Tanaka H, Yokomori T (2004) On the power of membrane division in P systems. J Theor Comput Sci 324(1):61–85

    Article  MATH  Google Scholar 

  • Petre I, Petre L (1999) Mobile ambients and P-systems. J Univers Comput Sci 9:588–598

    MathSciNet  Google Scholar 

  • Petri CA (1962) Kommunikation mit Automaten. Ph.D. Thesis, University of Bonn

  • Regev A, Panina EM, Silverman W, Cardelli L, Shapiro E (2004) BioAmbients: an abstraction for biological compartments. J Theor Comput Sci 325(1):141–167

    Article  MATH  MathSciNet  Google Scholar 

  • Schnoebelen Ph (2002) Verifying lossy channel systems has nonprimitive recursive complexity. Inform Process Lett 83(5):251–261

    Article  MATH  MathSciNet  Google Scholar 

  • Reisig W (1985) Petri nets—an introduction. Springer, Berlin

    MATH  Google Scholar 

  • The P Systems Webpage http://www.ppage.psystems.eu/

  • Zavattaro G (2009) Reachability analysis in bioambients. Electron Notes Theor Comput Sci 227:179–193

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Università di Genova, Genova, Italy

    Giorgio Delzanno

  2. Université Libre de Bruxelles, Brussels, Belgium

    Laurent Van Begin

Authors
  1. Giorgio Delzanno
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Laurent Van Begin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Giorgio Delzanno.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Delzanno, G., Begin, L.V. On the verification of membrane systems with dynamic structure. Nat Comput 9, 795–818 (2010). https://doi.org/10.1007/s11047-010-9214-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11047-010-9214-0

Keywords

Search

Navigation