Recently, we have introduced two graph-decomposition theorems based on a new graph product, motivated by applications in the context of synchronising periodic real-time processes. This vertexremoving synchronised product (VRSP) is based on modifications of the well-known Cartesian product and is closely related to the synchronised product due to Wohrle and Thomas. Here, we ¨ show how we can relax the requirements of these two graph-decomposition theorems.
Reading and writing is modelled in CSP using actions containing the symbols ? and !. These reading actions and writing actions are synchronous, and there is a one-to-one relationship between occurrences of pairs of these actions. In the CPA conference 2017, we introduced the extended half-synchronous al- phabetised parallel operator X ⇕ Y , which disconnects the writing to and reading from a channel in time; the reading processes are divided into sets which are set-wise asynchronous, but intra-set-wise synchronous, giving full flexibility to the reads. In this paper, we allow multiple writers to write to the same channel set-wise asynchronously, but intra-set-wise synchronously and we study the impact on our (Extended) Vertex Removing Synchronised Product. The advantages we accomplish are that the extension of X ⇕ Y gives more flexibility by indexing the writing actions and the reading actions, leading to a straightforward majority vote design. Furthermore, the extension of X ⇕ Y preserves the advantages of the X ⇕ Y operator.
Reading and writing is modelled in CSP using actions containing the symbols ? and !. These reading actions and writing actions are synchronous, and there is a one-to-one relationship between occurrences of pairs of these actions. In the CPA conference 2016, we introduced the half-synchronous alphabetised parallel operator X ⇓ Y , which disconnects the writing to and reading from a channel in time. We introduce in this paper an extension of X ⇓ Y , where the definition of X ⇓ Y is relaxed; the reading processes are divided into sets which are set-wise asynchronous, but intra-set-wise synchronous, giving full flexibility to the asynchronous writes and reads. Furthermore, we allow multiple writers to the same channel and we study the impact on a Vertex Removing Synchronised Product. The advantages we accomplish are that the extension of X ⇓ Y gives more flexibility by indexing the reading actions and allowing multiple write actions to the same channel. Furthermore, the extension of X ⇓Y reduces the end-to-end processing time of the processor or coprocessor in a distributed computing system. We show the effects of these advantages in a case study describing a Controlled Emergency Stop for a processor-coprocessor combination.
