UTP Semantics for BigrTiMo

  • Wanling Xie
  • Huibiao ZhuEmail author
  • Shengchao Qin
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11232)


BigrTiMo [1], a process algebra that combines the rTiMo calculus [2] and the Bigraph model [3], is capable of specifying a rich variety of properties for structure-aware mobile systems. Compared with rTiMo, our BigrTiMo calculus can specify not only time, mobility and local communication, but also remote communication. In this paper, we study the semantic foundation of this highly expressive modelling language and propose a denotational semantic model for it based on Hoare and He’s Unifying Theories of Programming (UTP) [4]. Compared to the standard UTP model, in addition to the communication, the novelty of the proposed UTP model in this paper covers time, location and global shared variable. Moreover, we give an example to show the contribution of BigrTiMo and illustrate how to use our semantic model and the trace-merging definition proposed in our paper under this example. We also demonstrate the proofs of some algebraic laws proposed in [1] based on our denotational semantics.



This work was partly supported by Shanghai Collaborative Innovation Center of Trustworthy Software for Internet of Things (No. ZF1213).


  1. 1.
    Xie, W., Zhu, H., Xu, Q.: BigrTiMo - a process algebra for structure-aware mobile systems. In: ICECCS 2017, Fukuoka, Japan, 6–8 November 2017, pp. 50–59 (2017)Google Scholar
  2. 2.
    Aman, B., Ciobanu, G.: Real-time migration properties of rTiMo verified in Uppaal. In: Hierons, R.M., Merayo, M.G., Bravetti, M. (eds.) SEFM 2013. LNCS, vol. 8137, pp. 31–45. Springer, Heidelberg (2013). Scholar
  3. 3.
    Milner, R.: The Space and Motion of Communicating Agents. Cambridge University Press, Cambridge (2009)CrossRefGoogle Scholar
  4. 4.
    Hoare, C.A.R., He, J.: Unifying Theories of Programming. Prentice Hall International Series in Computer Science. Prentice Hall, Upper Saddle River (1998)zbMATHGoogle Scholar
  5. 5.
    Ciobanu, G., Koutny, M.: Timed mobility in process algebra and Petri nets. J. Log. Algebr. Program. 80(7), 377–391 (2011)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Hoare, T.: Unifying semantics for concurrent programming. In: Coecke, B., Ong, L., Panangaden, P. (eds.) Computation, Logic, Games, and Quantum Foundations. The Many Facets of Samson Abramsky. LNCS, vol. 7860, pp. 139–149. Springer, Heidelberg (2013). Scholar
  7. 7.
    Xie, W., Xiang, S.: UTP semantics for rTiMo. In: Bowen, J.P., Zhu, H. (eds.) UTP 2016. LNCS, vol. 10134, pp. 176–196. Springer, Cham (2017). Scholar
  8. 8.
    Shi, L., Zhao, Y., Liu, Y., Sun, J., Dong, J.S., Qin, S.: A UTP semantics for communicating processes with shared variables. In: Groves, L., Sun, J. (eds.) ICFEM 2013. LNCS, vol. 8144, pp. 215–230. Springer, Heidelberg (2013). Scholar
  9. 9.
    Hoare, T., van Staden, S.: In praise of algebra. Formal Aspects Comput. 24(4–6), 423–431 (2012)MathSciNetCrossRefGoogle Scholar
  10. 10.
    He, J., Hoare, C.A.R.: From algebra to operational semantics. Inf. Process. Lett. 45(2), 75–80 (1993)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Shanghai Key Laboratory of Trustworthy Computing, School of Computer Science and Software EngineeringEast China Normal UniversityShanghaiChina
  2. 2.School of ComputingUniversity of TeessideMiddlesbrough, Tees ValleyUK

Personalised recommendations