A Framework for Certified Self-Stabilization

  • Karine AltisenEmail author
  • Pierre Corbineau
  • Stéphane Devismes
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9688)


We propose a framework to build certified proofs of self-stabilizing algorithms using the proof assistant Coq. We first define in Coq the locally shared memory model with composite atomicity, the most commonly used model in the self-stabilizing area. We then validate our framework by certifying a non-trivial part of an existing self-stabilizing algorithm which builds a k-hop dominating set of the network. We also certify a quantitative property related to its output: we show that the size of the computed k-hop dominating set is at most \(\lfloor \frac{n-1}{k+1} \rfloor + 1\), where n is the number of nodes. To obtain these results, we developed a library which contains general tools related to potential functions and cardinality of sets.


Span Tree Proof Assistant Regular Node Global Criterion Share Memory Model 
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  1. 1.
    Ben-Othman, J., Bessaoud, K., Bui, A., Pilard, L.: Self-stabilizing algorithm for efficient topology control in wireless sensor networks. J. Comput. Sci. 4(4), 199–208 (2013)CrossRefGoogle Scholar
  2. 2.
    Blanqui, F., Koprowski, A.: CoLoR: a coq library on well-founded rewrite relations and its application to the automated verification of termination certificates. Math. Struct. Comput. Sci. 21(4), 827–859 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Caron, E., Chuffart, F., Tedeschi, C.: When self-stabilization meets real platforms: an experimental study of a peer-to-peer service discovery system. future gener. comput. syst. 29(6), 1533–1543 (2013)CrossRefGoogle Scholar
  4. 4.
    Chen, M., Monin, J.F.: Formal verification of netlog protocols. In: TASE (2012)Google Scholar
  5. 5.
    Chen, N., Yu, H., Huang, S.: A self-stabilizing algorithm for constructing spanning trees. Inf. Process. Lett. 39, 147–151 (1991)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Courtieu, P.: Proving self-stabilization with a proof assistant. In: IPDPS (2002)Google Scholar
  7. 7.
    Courtieu, P., Rieg, L., Tixeuil, S., Urbain, X.: Impossibility of gathering, a certification. Inf. Process. Lett. 115(3), 447–452 (2015)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Datta, A.K., Larmore, L.L., Devismes, S., Heurtefeux, K., Rivierre, Y.: Competitive self-stabilizing k-clustering. In: ICDCS (2012)Google Scholar
  9. 9.
    Datta, A.K., Larmore, L.L., Devismes, S., Heurtefeux, K., Rivierre, Y.: Self-stabilizing small k-dominating sets. IJNC 3(1), 116–136 (2013)zbMATHGoogle Scholar
  10. 10.
    Deng, Y., Monin, J.F.: Verifying self-stabilizing population protocols with Coq. In: TASE (2009)Google Scholar
  11. 11.
    Dershowitz, N., Manna, Z.: Proving termination with multiset orderings. Commun. ACM 22(8), 465–476 (1979)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Dijkstra, E.W.: Self-stabilizing systems in spite of distributed control. Commun. ACM 17, 643–644 (1974)CrossRefzbMATHGoogle Scholar
  13. 13.
    Dolev, S., Gouda, M.G., Schneider, M.: Memory requirements for silent stabilization. In: PODC, pp. 27–34 (1996)Google Scholar
  14. 14.
    Ghosh, S.: An alternative solution to a problem on self-stabilization. ACM Trans. Program. Lang. Syst. 15(4), 735–742 (1993)CrossRefGoogle Scholar
  15. 15.
    Huang, S., Chen, N.: Self-stabilizing depth-first token circulation on networks. Distrib. Comput. 7(1), 61–66 (1993)CrossRefzbMATHGoogle Scholar
  16. 16.
    Küfner, P., Nestmann, U., Rickmann, C.: Formal verification of distributed algorithms. In: Baeten, J.C.M., Ball, T., de Boer, F.S. (eds.) TCS 2012. LNCS, vol. 7604, pp. 209–224. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  17. 17.
    Kulkarni, S.S., Rushby, J.M., Shankar, N.: A case-study in component-based mechanical verification of fault-tolerant programs. In: WSS, pp. 33–40 (1999)Google Scholar
  18. 18.
    Lamport, L.: How to write a 21st century proof. J. fixed point theory appl. 11(1), 43–63 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  19. 19.
    The Coq Development Team: The Coq Proof Assistant, Reference Manual.

Copyright information

© IFIP International Federation for Information Processing 2016

Authors and Affiliations

  • Karine Altisen
    • 1
    Email author
  • Pierre Corbineau
    • 1
  • Stéphane Devismes
    • 1
  1. 1.VERIMAG UMR 5104Université Grenoble AlpesGrenobleFrance

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