https://doi.org/10.30598/barekengvol18iss2pp1359-1368 June 2024 Volume 18 Issue 2 Page 1359–1368 P-ISSN: 1978-7227 E-ISSN: 2615-3017 BAREKENG: Journal of Mathematics and Its Applications 1359 PROVING THE CORRECTNESS OF THE EXTENDED SERIAL GRAPH-VALIDATION QUEUE SCHEME IN THE CLIENT- SERVER SYSTEM Fitra Nuvus Salsabila 1* , Fahren Bukhari 2 , Sri Nurdiati 3 1,2,3 Department of Mathematics, Faculty of Mathematics and Natural Sciences, IPB University Jln. Meranti Kampus, Babakan, Dramaga, Bogor 16680, Indonesia Corresponding author’s e-mail: * fitrasalsabila@apps.ipb.ac.id ABSTRACT Article History: Numerous studies have been conducted to develop concurrency control schemes that can be applied to client-server systems, such as the Extended Serial Graph-Validation Queue (SG- VQ) scheme. Extended SG-VQ is a control concurrency scheme in the client-server system that implements object caching on the client side and a locking strategy on the server side. This scheme employs validation algorithms based on queues on the client side and graphs on the server side. This research focuses on the mathematical analysis of the correctness of the Extended SG-VQ scheme using serializability as the criterion that needs to be achieved. Implementing a cycle-free transaction graph is a necessary and sufficient condition to achieve serializability. In this research, the serializability of the Extended SG-VQ scheme has been proven through the exposition of ten definitions, two propositions, three lemmas, and one theorem. Received: 28 th February 2024 Revised: 20 th March 2024 Accepted: 10 th May 2024 Published: 1 st June 2024 Keywords: Client-Server; Concurrency Control; Graph; Locking; Serializability. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-ShareAlike 4.0 International License. How to cite this article: F. N. Salsabila, F. Bukhari and S. Nurdiati., “PROVING CORRECTNESS OF THE EXTENDED SERIAL GRAPH-VALIDATION QUEUE SCHEME WITH MATHEMATICAL ANALYSYS,” BAREKENG: J. Math. & App., vol. 18, iss. 2, pp. 1359-1368, June, 2024. Copyright © 2024 Author(s) Journal homepage: https://ojs3.unpatti.ac.id/index.php/barekeng/ Journal e-mail: barekeng.math@yahoo.com; barekeng.journal@mail.unpatti.ac.id Research Article ∙ Open Access