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Symposium on Self-Stabilizing Systems

SSS 2012: Stabilization, Safety, and Security of Distributed Systems pp 77–89Cite as

Terminating Population Protocols via Some Minimal Global Knowledge Assumptions

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7596))

Abstract

We extend the population protocol model with a cover-time service that informs a walking state every time it covers the whole network. This is simply a known upper bound on the cover time of a random walk. This allows us to introduce termination into population protocols, a capability that is crucial for any distributed system. By reduction to an oracle-model we arrive at a very satisfactory lower bound on the computational power of the model: we prove that it is at least as strong as a Turing Machine of space logn with input commutativity, where n is the number of nodes in the network. We also give a logn-space, but nondeterministic this time, upper bound. Finally, we prove interesting similarities of this model to linear bounded automata.

This work has in part been supported by the EU (European Social Fund - ESF) and Greek national funds through (i) the Operational Programme “Education and Lifelong Learning” (EdLL), under the title “Foundations of Dynamic Distributed Computing Systems” (FOCUS), and (ii) the National Strategic Reference Framework (NSRF) (Regional Operational Programme - Western Greece) under the title “Advanced Systems and Services over Wireless and Mobile Networks” (number 312179).

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References

  1. Angluin, D., Aspnes, J., Chan, M., Fischer, M.J., Jiang, H., Peralta, R.: Stably Computable Properties of Network Graphs. In: Prasanna, V.K., Iyengar, S.S., Spirakis, P.G., Welsh, M. (eds.) DCOSS 2005. LNCS, vol. 3560, pp. 63–74. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  2. Angluin, D., Aspnes, J., Diamadi, Z., Fischer, M.J., Peralta, R.: Computation in networks of passively mobile finite-state sensors. Distributed Computing, 235–253 (2006)

    Google Scholar 

  3. Angluin, D., Aspnes, J., Eisenstat, D.: Fast computation by population protocols with a leader. Distributed Computing 21(3), 183–199 (2008)

    Article  Google Scholar 

  4. Angluin, D., Aspnes, J., Eisenstat, D., Ruppert, E.: The computational power of population protocols. Distributed Computing 20(4), 279–304 (2007)

    Article  Google Scholar 

  5. Beauquier, J., Burman, J., Clement, J., Kutten, S.: On utilizing speed in networks of mobile agents. In: Proceedings of the 29th ACM SIGACT-SIGOPS Symposium on Principles of Distributed Computing, PODC 2010, pp. 305–314. ACM, New York (2010)

    Chapter  Google Scholar 

  6. Chatzigiannakis, I., Michail, O., Nikolaou, S., Pavlogiannis, A., Spirakis, P.G.: Passively mobile communicating machines that use restricted space. Theor. Comput. Sci. 412(46), 6469–6483 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  7. Csuhaj-Varjú, E., Martín-Vide, C., Mitrana, V.: Multiset Automata. In: Calude, C.S., Pun, G., Rozenberg, G., Salomaa, A. (eds.) Multiset Processing. LNCS, vol. 2235, pp. 69–84. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  8. Edighoffer, J.L.: Distributed, replicated computer bulletin board service. PhD thesis, Stanford, CA, USA, UMI order no. GAX86-19742 (1986)

    Google Scholar 

  9. Fischer, M., Jiang, H.: Self-stabilizing Leader Election in Networks of Finite-State Anonymous Agents. In: Shvartsman, M.M.A.A. (ed.) OPODIS 2006. LNCS, vol. 4305, pp. 395–409. Springer, Heidelberg (2006), http://dx.doi.org/10.1007/11945529_28

    Chapter  Google Scholar 

  10. Fischer, P.C., Meyer, A.R., Rosenberg, A.L.: Counter machines and counter languages. Mathematical Systems Theory 2(3), 265–283 (1968)

    Article  MathSciNet  MATH  Google Scholar 

  11. Ginsburg, S., Spanier, E.H.: Semigroups, presburger formulas, and languages. Pacific Journal of Mathematics 16, 285–296 (1966)

    MathSciNet  MATH  Google Scholar 

  12. Ibarra, O.H.: On the computational complexity of membrane systems. Theor. Comput. Sci. 320, 89–109 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  13. Michail, O., Chatzigiannakis, I., Spirakis, P.G.: Mediated population protocols. Theor. Comput. Sci. 412, 2434–2450 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  14. Michail, O., Chatzigiannakis, I., Spirakis, P.G.: New Models for Population Protocols. In: Lynch, N.A. (ed.) Synthesis Lectures on Distributed Computing Theory. Morgan & Claypool (2011)

    Google Scholar 

  15. Minsky, M.L.: Recursive unsolvability of post’s problem of “tag” and other topics in theory of turing machines. The Annals of Mathematics 74(3), 437–455 (1961)

    Article  MathSciNet  MATH  Google Scholar 

  16. Savitch, W.J.: Relationships between nondeterministic and deterministic tape complexities. J. Comput. System Sci. 4(2), 177–192 (1970)

    Article  MathSciNet  MATH  Google Scholar 

  17. Vaszil, G.: Multiset grammars, multiset automata, and membrane systems. In: Colloquium on the Occasion of the 50th Birthday of Victor Mitrana, pp. 1–10. Springer (2008)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Computer Technology Institute & Press “Diophantus” (CTI), Patras, Greece

    Othon Michail, Ioannis Chatzigiannakis & Paul G. Spirakis

  2. Computer Engineering and Informatics Department (CEID), University of Patras, Greece

    Othon Michail, Ioannis Chatzigiannakis & Paul G. Spirakis

Authors
  1. Othon Michail
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  2. Ioannis Chatzigiannakis
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  3. Paul G. Spirakis
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Editor information

Editors and Affiliations

  1. School of Computing, Informatics, and Decision Systems Engineering, Arizona State University, 699 South Mill Avenue, 85281, Tempe, AZ, USA

    Andréa W. Richa

  2. Department of Computer Science, University of Paderborn, Fürstenallee 11, 33102, Paderborn, Germany

    Christian Scheideler

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© 2012 Springer-Verlag Berlin Heidelberg

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Michail, O., Chatzigiannakis, I., Spirakis, P.G. (2012). Terminating Population Protocols via Some Minimal Global Knowledge Assumptions. In: Richa, A.W., Scheideler, C. (eds) Stabilization, Safety, and Security of Distributed Systems. SSS 2012. Lecture Notes in Computer Science, vol 7596. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33536-5_8

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  • DOI: https://doi.org/10.1007/978-3-642-33536-5_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-33535-8

  • Online ISBN: 978-3-642-33536-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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