Distributed Computing

, Volume 18, Issue 4, pp 235–253 | Cite as

Computation in networks of passively mobile finite-state sensors

  • Dana Angluin
  • James Aspnes
  • Zoë Diamadi
  • Michael J. Fischer
  • René Peralta
Special Issue Podc 04

Abstract

The computational power of networks of small resource-limited mobile agents is explored. Two new models of computation based on pairwise interactions of finite-state agents in populations of finite but unbounded size are defined. With a fairness condition on interactions, the concept of stable computation of a function or predicate is defined. Protocols are given that stably compute any predicate in the class definable by formulas of Presburger arithmetic, which includes Boolean combinations of threshold-k, majority, and equivalence modulo m. All stably computable predicates are shown to be in NL. Assuming uniform random sampling of interacting pairs yields the model of conjugating automata. Any counter machine with O(1) counters of capacity O(n) can be simulated with high probability by a conjugating automaton in a population of size n. All predicates computable with high probability in this model are shown to be in P; they can also be computed by a randomized logspace machine in exponential time. Several open problems and promising future directions are discussed.

Keywords

Diffuse computation Finite-state agent Intermittent communication Mobile agent Sensor net Stable computation 

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References

  1. 1.
    Angluin, D., Aspnes, J., Chan, M., Fischer, M.J., Jiang, H., Peralta, R.: Stably computable properties of network graphs. In: Viktor K. Prasanna, Sitharama Iyengar, Paul Spirakis and Matt Welsh (eds.), Distributed Computing in Sensor Systems: First IEEE International Conference (2005). Lecture Notes in Computer Science 3560, 63–74 (June/July, 2005) Proceedings Marina del Rey, CA, USAGoogle Scholar
  2. 2.
    Angluin, D., Aspnes, J., Diamadi, Z., Fischer, M.J., Peralta, R.: Urn automata. Tech. Rep. YALEU/DCS/TR–1280, Yale University Department of Computer Science (2003)Google Scholar
  3. 3.
    Berry, G., Boudol, G.: The chemical abstract machine. Theor. Comp. Sci. 96, 217–248 (1992)CrossRefMathSciNetGoogle Scholar
  4. 4.
    Brand, D., Zafiropulo, P.: On communicating finite-state machines. J. ACM 30(2), 323–342 (1983)CrossRefMathSciNetGoogle Scholar
  5. 5.
    Diamadi, Z., Fischer, M.J.: A simple game for the study of trust in distributed systems. Wuhan Univ. J. Natur. Sci. 6(1–2), 72–82 (2001). Also appears as Yale Technical Report TR–1207, January 2001, available at URL ftp://ftp.cs.yale.edu/pub/TR/tr1207.psGoogle Scholar
  6. 6.
    Esparza, J.: Decidability and complexity of Petri net problems-an introduction. In: Rozenberg, G., Reisig, W., (eds.) Lectures on Petri Nets I: Basic models, pp. 374–428. Springer Verlag (1998). Published as LNCS 1491Google Scholar
  7. 7.
    Esparza, J., Nielsen, M.: Decibility issues for Petri nets—a survey. J. Inform. Process. Cybern. 30(3), 143–160 (1994)Google Scholar
  8. 8.
    Fang, Q., Zhao, F., Guibas, L.: Lightweight sensing and communication protocols for target enumeration and aggregation. In: Proceedings of the 4th ACM International Symposium on Mobile ad hoc Networking & Computing, pp. 165–176. ACM Press (2003)Google Scholar
  9. 9.
    Fischer, M.J., Rabin, M.O.: Super-exponential complexity of Presburger arithmetic. In: Complexity of Computation, SIAM-AMS Proceedings, vol. VII, pp. 27–41. American Mathematical Society (1974)Google Scholar
  10. 10.
    Ginsburg, S., Spanier, E.H.: Semigroups, Presburger formulas, and languages. Pac. J. Math. 16, 285–296 (1966)MathSciNetGoogle Scholar
  11. 11.
    Grossglauser, M., Tse, D.N.C.: Mobility increases the capacity of ad hoc wireless networks. IEEE/ACM Transac. Networking 10(4), 477–486 (2002)Google Scholar
  12. 12.
    Ibarra, O.H., Dang, Z., Egecioglu, O.: Catalytic p systems, semilinear sets, and vector addition systems. Theor. Comput. Sci. 312(2–3), 379–399 (2004)CrossRefMathSciNetGoogle Scholar
  13. 13.
    Immerman, N.: Nondeterministic space is closed under complementation. SIAM J. Comput. 17(5), 935–938 (1988)CrossRefMATHMathSciNetGoogle Scholar
  14. 14.
    Intanagonwiwat, C., Govindan, R., Estrin, D.: Directed diffusion: a scalable and robust communication paradigm for sensor networks. In: Proceedings of the 6th Annual International Conference on Mobile computing and networking, pp. 56–67. ACM Press (2000)Google Scholar
  15. 15.
    Kracht, M.: The Mathematics of Language, Studies in Generative Grammar, vol. 63. Mouton de Gruyter (2003). ISBN 3-11-017620-3Google Scholar
  16. 16.
    Madden, S.R., Franklin, M.J., Hellerstein, J.M., Hong, W.: TAG: A Tiny AGgregation service for ad-hoc sensor networks (December, 2002). In OSDI 2002: Fifth Symposium on Operating Systems Design and ImplementationGoogle Scholar
  17. 17.
    Milner, R.: Bigraphical reactive systems: basic theory. Tech. rep., University of Cambridge (2001). UCAM-CL-TR-523Google Scholar
  18. 18.
    Minsky, M.L.: Computation: Finite and Infinite Machines. Prentice-Hall Series in Automatic Computation. Prentice-Hall, Inc., Englewood Cliffs, N.J. (1967)Google Scholar
  19. 19.
    Monk, J.D.: Mathematical Logic. Springer, Berlin, Heidelberg (1976)Google Scholar
  20. 20.
    von Neumann, J.: Theory and organization of complicated automata. In: A.W. Burks (ed.) Theory of Self-Reproducing Automata [by] John von Neumann, pp. 29–87 (Part One). University of Illinois Press, Urbana (1949). Based on transcripts of lectures delivered at the University of Illinois, in December 1949. Edited for publication by A.W. BurksGoogle Scholar
  21. 21.
    Parikh, R.J.: On context-free languages. J. ACM 13(4), 570–581 (1966).CrossRefMATHMathSciNetGoogle Scholar
  22. 22.
    Presburger, M.: Über die Vollständigkeit eines gewissen Systems der Arithmetik ganzer Zahlen, in welchem die Addition als einzige Operation hervortritt. In: Comptes-Rendus du I Congrès de Mathématiciens des Pays Slaves, pp. 92–101. Warszawa (1929)Google Scholar
  23. 23.
    Volzer, H.: Randomized non-sequential processes. In: Proceedings of CONCUR 2001-Concurrency Theory, pp. 184–201 (2001)Google Scholar
  24. 24.
    Zhao, F., Liu, J., Liu, J., Guibas, L., Reich, J.: Collaborative signal and information processing: An information directed approach. Proc. IEEE 91(8), 1199–1209 (2003)Google Scholar

Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  • Dana Angluin
    • 1
  • James Aspnes
    • 1
  • Zoë Diamadi
    • 1
  • Michael J. Fischer
    • 1
  • René Peralta
    • 1
  1. 1.Department of Computer ScienceYale UniversityNew HavenUSA

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