Constraining Self-organisation Through Corridors of Correct Behaviour: The Restore Invariant Approach

  • Florian NafzEmail author
  • Hella Seebach
  • Jan-Philipp Steghöfer
  • Gerrit Anders
  • Wolfgang Reif
Part of the Autonomic Systems book series (ASYS, volume 1)


Self-organisation aspects and the large number of entities in Organic Computing (OC) systems make them extremely hard to predict and analyse. However, the application of OC principles to, e.g., safety critical systems, is usually not conceivable without behavioural guarantees. In this article, a rigorous approach called the Restore Invariant Approach is presented, which provides a specification paradigm and a formal framework that allows to give guarantees for a system despite of self-organisation. The approach provides a method for specifying unwanted system states by constraining the system and defining a corridor of correct behaviour. Furthermore, a decentralised algorithm for monitoring and restoring the invariant based on coalition formation is presented.


Self-organisation Formal verification Decentralised algorithms 


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  1. 1.
    Ackermann, J.: Formal description of OCL specification patterns for behavioral specification of software components. In: Workshop on Tool Support for OCL and Related Formalisms, Technical Report LGL-REPORT-2005-001, pp. 15–29, EPFL (2005) Google Scholar
  2. 2.
    Anders, G., Seebach, H., Nafz, F., Steghöfer, J.-P., Reif, W.: Decentralized reconfiguration for self-organizing resource-flow systems based on local knowledge. In: Proceedings of EASe 2011, Las Vegas, USA (2011, to appear) Google Scholar
  3. 3.
    Balser, M., Reif, W., Schellhorn, G., Stenzel, K.: KIV 3.0 for provably correct systems. In: Hutter, D., Stephan, W., Traverso, P., Ullmann, M. (eds.) Proc. Int. Wsh. Applied Formal Methods. LNCS, vol. 1641, pp. 330–337. Springer, Berlin (1999) Google Scholar
  4. 4.
    Bäumler, S., Balser, M., Nafz, F., Reif, W., Schellhorn, G.: Interactive verification of concurrent systems using symbolic execution. AI Commun. 23(2–3), 285–307 (2010) MathSciNetzbMATHGoogle Scholar
  5. 5.
    Blum, M., Kanna, S.: Designing programs that check their work. In: STOC ’89: Proceedings of the Twenty-First Annual ACM Symposium on Theory of Computing, pp. 86–97. ACM, New York (1989) CrossRefGoogle Scholar
  6. 6.
    Branke, J., Mnif, M., Müller-Schloer, C., Prothmann, H., Richter, U., Rochner, F., Schmeck, H.: Organic computing—addressing complexity by controlled self-organization. In: ISoLA, pp. 185–191 (2006) Google Scholar
  7. 7.
    Goldberg, D.E.: Genetic Algorithms in Search, Optimization, and Machine Learning, 1st edn. Addison-Wesley, Reading (1989) zbMATHGoogle Scholar
  8. 8.
    Güdemann, M., Ortmeier, F., Reif, W.: Safety and dependability analysis of self-adaptive systems. In: Proceedings of ISoLA 2006. IEEE Comput. Soc., Los Alamitos (2006) Google Scholar
  9. 9.
    Nafz, F., Ortmeier, F., Seebach, H., Steghöfer, J.-P., Reif, W.: A universal self-organization mechanism for role-based organic computing systems. In: González Nieto, J., Reif, W., Wang, G., Indulska, J. (eds.) Autonomic and Trusted Computing. LNCS, vol. 5586, pp. 17–31. Springer, Berlin (2009) CrossRefGoogle Scholar
  10. 10.
    Nafz, F., Seebach, H., Steghöfer, J.-P., Bäumler, S., Reif, W.: A formal framework for compositional verification of organic computing systems. In: Xie, B., Branke, J., Sadjadi, S., Zhang, D., Zhou, X. (eds.) Autonomic and Trusted Computing. LNCS, vol. 6407, pp. 17–31. Springer, Berlin (2010) CrossRefGoogle Scholar
  11. 11.
    Rahwan, T., Ramchurn, S., Jennings, N., Giovannucci, A.: An anytime algorithm for optimal coalition structure generation. J. Artif. Intell. Res. 34(1), 521–567 (2009) MathSciNetzbMATHGoogle Scholar
  12. 12.
    Richter, U., Mnif, M., Branke, J., Müller-Schloer, C., Schmeck, H.: Towards a generic observer/controller architecture for Organic Computing. INFORMATIK 2006 – Informatik für Menschen! P-93, pp. 112–119 (2006) Google Scholar
  13. 13.
    Shehory, O., Kraus, S.: Methods for task allocation via agent coalition formation. Artif. Intell. 101(1–2), 165–200 (1998) MathSciNetzbMATHCrossRefGoogle Scholar
  14. 14.
    Torlak, E., Jackson, D.: Kodkod: a relational model finder. In: Grumberg, O., Huth, M. (eds.) Tools and Algorithms for the Construction and Analysis of Systems. LNCS, vol. 4424, pp. 632–647. Springer, Berlin (2007). CrossRefGoogle Scholar
  15. 15.
    Tsang, E.: A Glimpse of constraint satisfaction. Artif. Intell. Rev. 13, 215–227 (1999) CrossRefGoogle Scholar

Copyright information

© Springer Basel AG 2011

Authors and Affiliations

  • Florian Nafz
    • 1
    Email author
  • Hella Seebach
    • 1
  • Jan-Philipp Steghöfer
    • 1
  • Gerrit Anders
    • 1
  • Wolfgang Reif
    • 1
  1. 1.Institute for Software & Systems EngineeringUniversität AugsburgAugsburgGermany

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