Skip to main content
SpringerLink
Log in
Book cover

International Workshop on Descriptional Complexity of Formal Systems

DCFS 2014: Descriptional Complexity of Formal Systems pp 114–125Cite as

Cycles and Global Attractors of Reaction Systems

  • Conference paper

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8614))

Abstract

Reaction systems are a recent formal model inspired by the chemical reactions that happen inside cells and possess many different dynamical behaviours. In this work we continue a recent investigation of the complexity of detecting some interesting dynamical behaviours in reaction system. We prove that detecting global behaviours such as the presence of global attractors is PSPACE - complete. Deciding the presence of cycles in the dynamics and many other related problems are also PSPACE - complete. Deciding bijectivity is, on the other hand, a coNP - complete problem.

This work has been supported by the French National Research Agency project EMC (ANR-09-BLAN-0164) and by Fondo d’Ateneo (FA) 2013 of Università degli Studi di Milano-Bicocca: “Complessità computazionale in modelli di calcolo bioispirati: Sistemi a membrane e sistemi a reazioni”.

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

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Barrett, C.L., Hunt III, H.B., Marathe, M.V., Ravi, S., Rosenkrantz, D.J., Stearns, R.E.: Complexity of reachability problems for finite discrete dynamical systems. Int. J. Found. Comput. Sci. 72(8), 1317–1345 (2006)

    MATH  MathSciNet  Google Scholar 

  2. Brijder, R., Ehrenfeucht, A., Rozenberg, G.: Reaction systems with duration. In: Kelemen, J., Kelemenová, A. (eds.) Pǎun Festschrif. LNCS, vol. 6610, pp. 191–202. Springer, Heidelberg (2011)

    Google Scholar 

  3. Corolli, L., Maj, C., Marini, F., Besozzi, D., Mauri, G.: An excursion in reaction systems: From computer science to biology. Theor. Comp. Sci. 454, 95–108 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  4. Ehrenfeucht, A., Main, M., Rozenberg, G.: Combinatorics of life and death for reaction systems. Int. J. Found. Comput. Sci. 21(03), 345–356 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  5. Ehrenfeucht, A., Main, M., Rozenberg, G.: Functions defined by reaction systems. Int. J. Found. Comput. Sci. 22(1), 167–168 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  6. Ehrenfeucht, A., Rozenberg, G.: Reaction systems. Fundam. Inform. 75, 263–280 (2007)

    MATH  MathSciNet  Google Scholar 

  7. Formenti, E., Manzoni, L., Porreca, A.E.: Fixed points and attractors of reaction systems. In: Beckmann, A., Csuhaj-Varjú, E., Meer, K. (eds.) CiE 2014. LNCS, vol. 8493, pp. 194–203. Springer, Heidelberg (2014)

    Chapter  Google Scholar 

  8. Hopcroft, J.E., Motwani, R., Ullman, J.D.: Introduction to Automata Theory, Languages, and Computation. Addison-Wesley (1979)

    Google Scholar 

  9. Immerman, N.: Descriptive Complexity. Graduate Texts in Computer Science. Springer (1999)

    Google Scholar 

  10. Kauffman, S.A.: Metabolic stability and epigenesis in randomly constructed genetic nets. J. Theor. Biol. 22(3), 437–467 (1969)

    Article  Google Scholar 

  11. Papadimitriou, C.H.: Computational Complexity. Addison-Wesley (1993)

    Google Scholar 

  12. Păun, G.: Computing with membranes. Journal of Computer and System Sciences 61(1), 108–143 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  13. Salomaa, A.: Functions and sequences generated by reaction systems. Theoretical Computer Science 466, 87–96 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  14. Salomaa, A.: Functional constructions between reaction systems and propositional logic. Int. J. Found. Comput. Sci. 24(1), 147–159 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  15. Salomaa, A.: Minimal and almost minimal reaction systems. Natural Computing 12(3), 369–376 (2013)

    Article  MathSciNet  Google Scholar 

  16. Shmulevich, I., Dougherty, E.R.: Probabilistic boolean networks: the modeling and control of gene regulatory networks. SIAM (2010)

    Google Scholar 

  17. Soloveichik, D., Cook, M., Winfree, E., Bruck, J.: Computation with finite stochastic chemical reaction networks. Natural Computing 7, 615–633 (2008)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Univ. Nice Sophia Antipolis, CNRS, I3S, UMR 7271, 06900, Sophia Antipolis, France

    Enrico Formenti & Luca Manzoni

  2. Dipartimento di Informatica, Sistemistica e Comunicazione, Università degli Studi di Milano-Bicocca, Viale Sarca 336/14, 20126, Milano, Italy

    Antonio E. Porreca

Authors
  1. Enrico Formenti
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Luca Manzoni
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Antonio E. Porreca
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Computer Science, The University of Western Ontario, N6A 5B7, London, Ontario, Canada

    Helmut Jürgensen

  2. Department of Mathematics and TUCS, University of Turku, 20014, Turku, Finland

    Juhani Karhumäki

  3. University of Turku, Fi-20014, Turku, Finland

    Alexander Okhotin

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer International Publishing Switzerland

About this paper

Cite this paper

Formenti, E., Manzoni, L., Porreca, A.E. (2014). Cycles and Global Attractors of Reaction Systems. In: Jürgensen, H., Karhumäki, J., Okhotin, A. (eds) Descriptional Complexity of Formal Systems. DCFS 2014. Lecture Notes in Computer Science, vol 8614. Springer, Cham. https://doi.org/10.1007/978-3-319-09704-6_11

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-09704-6_11

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-09703-9

  • Online ISBN: 978-3-319-09704-6

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation