Title: Linear polynomial algebra migration system for program equivalence and approximate optimisation

Authors: Weiwen Ge; Weidong Tang; Meiling Liu

Addresses: College of Physics and Electronic Information, Guangxi Minzu University, Nanning, Guangxi, 530006, China ' College of Artificial Intelligence, Guangxi Minzu University, Nanning, Guangxi, 530006, China ' College of Artificial Intelligence, Guangxi Minzu University, Nanning, Guangxi, 530006, China

Abstract: Program structure simplification constitutes a critical research domain in software engineering. With increasing system complexity, traditional simplification approaches remain predominantly confined to deterministic equivalence verification, lacking substantial investigation into approximate equivalence, error quantification, and control mechanisms. This paper develops a novel concept of common algebraic set bisimulation equivalence by integrating Wu's characteristic series within a linear polynomial algebraic migration system framework. To address non-deterministic equivalence problems, this work introduces novel least squares solution metrics and singular value thresholding control mechanisms. These innovations establish an approximate bisimulation equivalence theory that quantifies program behavior differences while maintaining controllable error bounds. Consequently, approximately equivalent systems can replace the original complex systems, thereby simplifying program architecture. Experimental validation using a concurrent communication program demonstrates the efficacy of our proposed methodology in program optimisation.

Keywords: Wu's characteristic series; linear polynomial algebra migration system; least squares solution; singular value thresholding; approximate bisimulation equivalence.

DOI: 10.1504/IJCSM.2025.149893

International Journal of Computing Science and Mathematics, 2025 Vol.22 No.2, pp.140 - 153

Received: 24 Nov 2024
Accepted: 05 Jul 2025
Published online: 17 Nov 2025 *

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