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.

中文翻译：

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一种移动系统的过程演算BigrTiMo及其形式语义

在本文中，我们提出了一种称为 BigrTiMo 的过程演算，它结合了 rTiMo 演算和 Bigraph 模型。BigrTiMo 演算能够为结构感知移动系统指定丰富多样的属性。与 rTiMo 相比，我们的 BigrTiMo 演算不仅可以指定时间、移动性和本地通信，还可以指定远程通信。然后，我们研究 BigrTiMo 演算的操作语义，并以一种名为 Maude 的声明性语言开发 BigrTiMo 演算的可执行正式规范。此外，我们使用 Maude 中的状态探索和 LTL 模型检查来验证 BigrTiMo 描述的移动系统的安全特性和活性特性。基于 Hoare 和 He 的统一编程理论 (UTP)，我们研究了这种高度表达建模语言的语义基础，并为其提出了指称语义模型和一组代数定律。本文的语义模型同时涵盖了时间、位置、通信和全局共享变量。我们还根据我们的指称语义证明了一些代数定律的证明。此外，我们通过研究从代数语义中推导出操作语义和指称语义来探索代数语义与操作语义和指称语义的关系。我们证明了派生的转换系统（例如，操作语义）和派生策略之间的等价性，这表明操作语义是健全和完整的。