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A process calculus BigrTiMo of mobile systems and its formal semantics

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Formal Aspects of Computing

Abstract

In this paper, we present a process calculus called BigrTiMo that combines the rTiMo calculus and the Bigraph model. BigrTiMo calculus 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. We then investigate the operational semantics of the BigrTiMo calculus and develop an executable formal specification of our BigrTiMo calculus in a declarative language called Maude. In addition, we verify safety properties and liveness properties of the mobile systems described by BigrTiMo using state exploration and LTL model checking in Maude. Based on Hoare and He's Unifying Theories of Programming (UTP), we study the semantic foundation of this highly expressive modelling language and propose a denotational semantic model and a set of algebraic laws for it. The semantic model in this paper covers time, location, communication and global shared variable at the same time. We also demonstrate the proofs of some algebraic laws based on our denotational semantics. Moreover, we explore how the algebraic semantics relates with the operational semantics and denotational semantics, which is conducted by the study of deriving the operational semantics and denotational semantics from algebraic semantics. We prove the equivalence between the derived transition system (e.g., the operational semantics) and the derivation strategy, which indicates that the operational semantics is sound and complete.

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Acknowledgements

This work was partly supported by National Key Research and Development Program of China (Grant No. 2018YFB2101300), National Natural Science Foundation of China (Grant No. 61872145, 62032024), Shanghai Collaborative Innovation Center of Trustworthy Software for Internet of Things (Grant No. ZF1213) and the Fundamental Research Funds for the Central Universities of China.

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  1. College of Computer Science and Technology, Nanjing University of Aeronautics and Astronautics, Nanjing, China

    Wanling Xie

  2. Shanghai Key Laboratory of Trustworthy Computing, East China Normal University, Shanghai, China

    Huibiao Zhu

  3. Faculty of Science and Technology, University of Macau, Macau, China

    Qiwen Xu

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  1. Wanling Xie
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Correspondence to Huibiao Zhu.

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Jin Song Dong

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Xie, W., Zhu, H. & Xu, Q. A process calculus BigrTiMo of mobile systems and its formal semantics. Form Asp Comp 33, 207–249 (2021). https://doi.org/10.1007/s00165-021-00530-x

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