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2018 | OriginalPaper | Buchkapitel

Two Approaches to Modelling Logical Time in Cyber-Physical Systems

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Abstract

The paper is devoted to problems caused by the nonlinearity of logical time in distributed, especially cyber-physical, systems. Two approaches to the modelling of such systems are considered in the paper. The operational approach is based on the traditional model that defines the admissible system behaviour as a set of acceptable schedules of the system. The paper argues in favour of restricting possible sets of schedules by that sets of schedules that satisfy certain safety properties. The denotational approach is stated in the language of category theory. This abstraction level clarifies concepts used in the models. In particular, it is explained the feature of linear models as terminal objects with respect to some natural class of morphisms. Further, the interrelation between these two approaches is represented as a formal relation and discuss some properties of the relation that need to be studied.

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Fußnoten
1
Usually, one uses the term clock structure if C is uniquely determined by the context.
 
2
The necessary definitions and results from the theory of categories can be found in [10].
 
3
Symbolically, \(\mathcal {S}\models P\).
 
Literatur
2.
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Zurück zum Zitat Cristian, F.: Probabilistic clock synchronization. Distrib. Comput. 3, 146–158 (1989)CrossRefMATH Cristian, F.: Probabilistic clock synchronization. Distrib. Comput. 3, 146–158 (1989)CrossRefMATH
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Zurück zum Zitat Kshemkalyani, A.D., Singhal, M.: Distributed Computing: Principles, Algorithms, and Systems. Cambridge University Press, Cambridge (2008)CrossRefMATH Kshemkalyani, A.D., Singhal, M.: Distributed Computing: Principles, Algorithms, and Systems. Cambridge University Press, Cambridge (2008)CrossRefMATH
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Zurück zum Zitat Lamport, L.: Time, clocks, and the ordering of events in a distributed system. CACM 21(7), 558–565 (1978)CrossRefMATH Lamport, L.: Time, clocks, and the ordering of events in a distributed system. CACM 21(7), 558–565 (1978)CrossRefMATH
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Zurück zum Zitat Mallet, F.: Clock constraint specification language: specifying clock constraints with UML/MARTE. Innov. Syst. Softw. Eng. 4(3), 309–314 (2008)CrossRef Mallet, F.: Clock constraint specification language: specifying clock constraints with UML/MARTE. Innov. Syst. Softw. Eng. 4(3), 309–314 (2008)CrossRef
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Zurück zum Zitat UML Profile for MARTE: Modeling and Analysis of Real-Time Embedded Systems. Formal/2011-06-03. OMG (2011) UML Profile for MARTE: Modeling and Analysis of Real-Time Embedded Systems. Formal/2011-06-03. OMG (2011)
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Zurück zum Zitat The National Science Foundation: Cyber-Physical Systems (CPS). Program Solicitation NSF 12–520. NSF, Arlington, VA (2012) The National Science Foundation: Cyber-Physical Systems (CPS). Program Solicitation NSF 12–520. NSF, Arlington, VA (2012)
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Zurück zum Zitat The National Science Foundation: Cyber-Physical Systems (CPS). Program Solicitation NSF 17–529. NSF, Arlington, VA (2017) The National Science Foundation: Cyber-Physical Systems (CPS). Program Solicitation NSF 17–529. NSF, Arlington, VA (2017)
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Zurück zum Zitat Willard, S.: General Topology. Dover Publication Inc., Mineola (1998)MATH Willard, S.: General Topology. Dover Publication Inc., Mineola (1998)MATH
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Zurück zum Zitat 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, vol. 1844, pp. 488–503. CEUR-WS (2017) 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, vol. 1844, pp. 488–503. CEUR-WS (2017)
18.
Zurück zum Zitat Zholtkevych, G., Mallet, F., Zaretska, I., Zholtkevych, G.: Two semantic models for clock relations in the clock constraint specification language. In: Ermolayev, V., Mayr, H.C., Nikitchenko, M., Spivakovsky, A., Zholtkevych, G. (eds.) ICTERI 2013. CCIS, vol. 412, pp. 190–209. Springer, Cham (2013). https://doi.org/10.1007/978-3-319-03998-5_10 Zholtkevych, G., Mallet, F., Zaretska, I., Zholtkevych, G.: Two semantic models for clock relations in the clock constraint specification language. In: Ermolayev, V., Mayr, H.C., Nikitchenko, M., Spivakovsky, A., Zholtkevych, G. (eds.) ICTERI 2013. CCIS, vol. 412, pp. 190–209. Springer, Cham (2013). https://​doi.​org/​10.​1007/​978-3-319-03998-5_​10
Metadaten
Titel
Two Approaches to Modelling Logical Time in Cyber-Physical Systems
verfasst von
Grygoriy Zholtkevych
Hassan Khalil El Zein
Copyright-Jahr
2018
DOI
https://doi.org/10.1007/978-3-319-76168-8_2

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