Informatics and Applications
2025, Volume 19, Issue 1, pp 2-8
UNIVERSAL CONSTRUCTIONS IN ALGEBRAIC SPECIFICATION OF DISTRIBUTED SYSTEMS
Abstract
The paper presents recent developments in the previously proposed generalized approach to algebraic specification of distributed systems based on the novel category-theoretic construction called graphalgebra. The graphalgebraic specification is based upon a directed multigraph, the edges of which represent computational operations performed in the nodes of the system and the vertices denote the data exchange ports between the components. Thus, deployment of operations upon the system nodes is specified explicitly. It is also advisable to explicitly describe, in the language of graphalgebras, the procedures for constructing systems towards the target deployment. To this end, the paper defines the constructions of subgraphalgebra, quotient graphalgebra, and bisimulation of graphalgebras and proves their key properties for the first time. The means to construct limits and colimits of suitable diagrams of graphalgebras are proposed. The theoretical results are illustrated by an example of calculating a limit in the category of deep neural networks.
[+] References (10)
- Sannella, D., and A. Tarlecki. 2012. Foundations of algebraic specification and formal software development. New York, NY: Springer. 584 p. doi: 10.1007/978-3-642- 17336-3.
- Pinus, A. G. 2021. Osnovy universal'noy algebry [Foundations of universal algebra]. Moscow: KNORUS. 182 p.
- Kovalyov, S.P. 2022. Algebraicheskaya spetsifikatsiya grafovykh vychislitel'nykh struktur [Algebraic specification of graph computational structures]. Informatika i ee
Primeneniya - Inform. Appl. 16(1):2-9. doi: 10.14357/ 19922264220101. EDN: GXHPZI.
- Kovalyov, S. P. 2024. Algebraicheskaya spetsifikatsiya raspredelennykh sistem s izmenyayushcheysya arkhitekturoy [Algebraic specification of graph computational structures]. Informatika i ee Primeneniya - Inform. Appl. 18(1):11-17.doi: 10.14357/19922264240102. EDN: MZAHBS.
- Adamek, J., H. Herrlich, and G.E. Strecker. 1990. Abstract and concrete categories. New York, NY: John Wiley. 507 p.
- Voutsadakis, G. 2010. Universal dialgebra: Unifying universal algebra and coalgebra. Far East J. Mathematical Sciences 44(1):1-53.
- Mac Lane, S. 1978. Categories for the working mathematician. New York, NY: Springer. 317 p.
- Shiebler, D., B. Gavranovic, and P W. Wilson. 2021. Category theory in machine learning. Cornell University. 43 p.
Availableat: https://arxiv.org/pdf/2106.07032 (accessed January 30, 2025).
- Adamek, J. 2005. Introduction to coalgebra. Theor. Appl. Categ. 14(8):157-199.
- Kovalyov, S. P 2016. Category-theoretic approach to software systems design. J. Mathematical Sciences 214(6):814- 853. doi: 10.1007/s10958-016-2814-1.
[+] About this article
Title
UNIVERSAL CONSTRUCTIONS IN ALGEBRAIC SPECIFICATION OF DISTRIBUTED SYSTEMS
Journal
Informatics and Applications
2025, Volume 19, Issue 1, pp 2-8
Cover Date
2025-04-01
DOI
10.14357/19922264250101
Print ISSN
1992-2264
Publisher
Institute of Informatics Problems, Russian Academy of Sciences
Additional Links
Key words
algebraic specification; distributed system; universal algebra; category theory; graphalgebra; subalgebara; bisimulation
Authors
S. P. Kovalyov 
Author Affiliations
V. A. Trapeznikov Institute of Control Sciences of the Russian Academy of Sciences, 65 Profsoyuznaya Str., Moscow 117997, Russian Federation
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