Category Methods for Modelling Logical Time Based on the Concept of Clocks
This paper continues a series of articles presenting authors’ ideas and results relating to development of category-theoretic methods for specifying and analysing models of logical time in distributed systems including cyber-physical systems. Results of this paper generalise results of the previous articles by the way of generalising the concepts of a clock structure and a schedule. The paper shows that all the main results obtained earlier remain valid for the generalisation under consideration. In addition, the proposed generalisation gives a tool for identifying in category-theoretic terms the concepts of global clocks and synchronisation processes.
KeywordsCategory Morphism Functor Equivalence of categories Logical time Logical clock Schedule Clock structure Clock morphism Schedule morphism Global clock Synchronising morphism
- 1.UML profile for MARTE: Modeling and Analysis of Real-Time Embedded Systems. Specification Formal/2011-06-03, OMG (2011)Google Scholar
- 2.André, C., Mallet, F.: Clock constraints in UML MARTE CCSL. Research Report RR-6540, INRIA (2008)Google Scholar
- 7.Novikov, B.: Lecture Notes on Category Theory. Luhansk National Pedagogical University (2004)Google Scholar
- 8.Zholtkevych, G., El Zein, H.K.: Logical time models to study cyber-physical systems. In: Ermolayev, V., et al. (eds.) Information and Communication Technologies in Education, Research, and Industrial Applications. Integration, Harmonization and Knowledge Transfer. Workshop Proceedings, vol. 1844. CEUR-WS, May 2017Google Scholar
- 10.Zholtkevych, G., El Zein, H.K., Polyakova, L.: Category methods for analysis of two approaches to modelling logical time based on concept of clocks. In: Ermolayev, V., et al. (eds.) Information and Communication Technologies in Education, Research, and Industrial Applications, vol. 2104, no. 2, pp. 696–706. CEUR-WS (2018)Google Scholar