Event algebra for transition systems composition application to timed automata

Formal specification languages have a lot of notions in common. They all introduce entities usually called processes, offer similar operators, and most importantly define their operational semantics based on labelled transition systems (LTS). However, each language defines specific synchronizing and/or memory structures. For instance, in CSP, the synchronization is defined between identical events, while in CCS and in synchronization vectors-based views it is defined respectively between complementary events or between possibly different events. In this paper, we aim at capturing some similarities of specification languages by defining a label-based formal framework for reasoning on LTS, their semantics and related properties. Firstly, we define a high-level synchronization mechanism in the form of an abstract label structure and identify some properties. Then, we introduce operators for composing and transforming label structures, study their intrinsic properties and explore how label structure properties propagate. Secondly, we introduce a LTS-based behavioral framework. We then lift the label structure composition and transformation operators to the LTS level and establish LTS-related properties derived from those of their underlying labelled structures. Thirdly, we consider extended transition systems, more specifically timed automata, as LTS built on top of specific labelled structures. Their semantics is reconstructed by applying operators of our framework on the syntactic LTS, which allows the direct proof of some semantic properties such as compositionality.