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International Workshop on Structured Object-Oriented Formal Language and Method

SOFL+MSVL 2016: Structured Object-Oriented Formal Language and Method pp 201–219Cite as

Model Checking of a Mobile Robots Perpetual Exploration Algorithm

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10189))

Abstract

Distributed mobile computing has been recently an active field of research, resulting in a large number of algorithms. However, to the best of our knowledge, few of the designed algorithms have been formally model checked. This paper presents a case study of how to specify and model check a given robot algorithm. We specify the system in Maude, a rewriting logic-based programming and specification language. To check the correctness of the algorithm, we express in LTL the properties it should enjoy. Our analysis leads to a counterexample which implies that the proposed algorithm is not correct.

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Notes

  1. 1.

    We confirm the incorrectness of the algorithm by obtaining the same counter-example. Any other result would be worrisome.

  2. 2.

    It is natural to consider 3-robot algorithms, since, for non-trivial rings, any exploration algorithm requires at least three robots.

  3. 3.

    On Fig. 3, the computed move is anti-clockwise.

  4. 4.

    The terminology comes from the Self-Stabilization concept. One can understand such configurations as “good” configurations.

  5. 5.

    Pictures represent a ring of size 14, but the rules are defined for arbitrary size, as written in the corresponding captions.

  6. 6.

    When two robots are located on the same nodes, there is no order.

References

  1. Bae, K., Meseguer, J.: Model checking linear temporal logic of rewriting formulas under localized fairness. Sci. Comput. Program. 99, 193–234 (2015)

    Article  Google Scholar 

  2. Bérard, B., Lafourcade, P., Millet, L., Potop-Butucaru, M., Thierry-Mieg, Y., Tixeuil, S.: Formal verification of mobile robot protocols. Distrib. Comput. 29, 1–29 (2016). (to appear, published online)

    Article  MathSciNet  Google Scholar 

  3. Blin, L., Milani, A., Potop-Butucaru, M., Tixeuil, S.: Exclusive perpetual ring exploration without chirality. In: Lynch, N.A., Shvartsman, A.A. (eds.) DISC 2010. LNCS, vol. 6343, pp. 312–327. Springer, Heidelberg (2010). doi:10.1007/978-3-642-15763-9_29

    Chapter  Google Scholar 

  4. Bonnet, F., Potop-Butucaru, M., Tixeuil, S.: Asynchronous gathering in rings with 4 robots. In: Mitton, N., Loscri, V., Mouradian, A. (eds.) ADHOC-NOW 2016. LNCS, vol. 9724, pp. 311–324. Springer, Cham (2016). doi:10.1007/978-3-319-40509-4_22

    Chapter  Google Scholar 

  5. Clavel, M., Durán, F., Eker, S., Lincoln, P., Martí-Oliet, N., Meseguer, J., Talcott, C.: All About Maude - A High-Performance Logical Framework. LNCS, vol. 4350. Springer, Heidelberg (2007)

    MATH  Google Scholar 

  6. D’Angelo, G., Di Stefano, G., Navarra, A., Nisse, N., Suchan, K.: Computing on rings by oblivious robots: a unified approach for different tasks. Algorithmica 72(4), 1055–1096 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  7. Flocchini, P., Prencipe, G., Santoro, N.: Distributed Computing by Oblivious Mobile Robots. Morgan & Claypool Publishers, San Rafael (2012)

    MATH  Google Scholar 

  8. Huth, M., Ryan, M.: Logic in Computer Science: Modelling and Reasoning about Systems. Cambridge University Press, Cambridge (2004)

    Book  MATH  Google Scholar 

  9. Kawamura, A., Kobayashi, Y.: Fence patrolling by mobile agents with distinct speeds. Distrib. Comput. 28(2), 147–154 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  10. Suzuki, I., Yamashita, M.: Distributed anonymous mobile robots: formation of geometric patterns. SIAM J. Comput. 28(4), 1347–1363 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  11. Yamauchi, Y., Uehara, T., Kijima, S., Yamashita, M.: Plane formation by synchronous mobile robots in the three dimensional Euclidean space. In: Moses, Y. (ed.) DISC 2015. LNCS, vol. 9363, pp. 93–106. Springer, Heidelberg (2015). doi:10.1007/978-3-662-48653-5_7

    Chapter  Google Scholar 

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Acknowledgments

The authors would like to thank Adrián Riesco for his useful comments on the specification in Maude. This work has been partially supported by Kakenhi 26540024 and 26240008.

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Authors and Affiliations

  1. School of Information Science, JAIST, Nomi, Japan

    Ha Thi Thu Doan, François Bonnet & Kazuhiro Ogata

Authors
  1. Ha Thi Thu Doan
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  2. François Bonnet
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  3. Kazuhiro Ogata
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Corresponding author

Correspondence to Ha Thi Thu Doan .

Editor information

Editors and Affiliations

  1. Hosei University, Tokyo, Japan

    Shaoying Liu

  2. Xidian University, Xi'an, Shaanxi, China

    Zhenhua Duan

  3. Xidian University, Xi'an, China

    Cong Tian

  4. Nihon University, Tokyo, Japan

    Fumiko Nagoya

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Doan, H.T.T., Bonnet, F., Ogata, K. (2017). Model Checking of a Mobile Robots Perpetual Exploration Algorithm. In: Liu, S., Duan, Z., Tian, C., Nagoya, F. (eds) Structured Object-Oriented Formal Language and Method. SOFL+MSVL 2016. Lecture Notes in Computer Science(), vol 10189. Springer, Cham. https://doi.org/10.1007/978-3-319-57708-1_12

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  • DOI: https://doi.org/10.1007/978-3-319-57708-1_12

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-57707-4

  • Online ISBN: 978-3-319-57708-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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