Title: Non-commutative Geometry for Computational Complexity Analysis

Jincheng Zhang

Published Sep 3, 2026• 0 citations

Abstract

This paper explores the potential of non-commutative geometry as a novel framework for analyzing the complexity of algorithms, offering a departure from traditional approaches. We propose a new mathematical model that utilizes geometric representations of computation, emphasizing the inherent order of operations and their impact on algorithm complexity. The core mechanism involves constructing a geometric structure that reflects the computational process, allowing for a deeper understanding of limitations in parallel computing and the design of more efficient algorithms. We demonstrate the framework's ability to reveal subtle complexities not readily apparent through standard complexity theory. This research aims to provide a fundamentally different perspective on algorithm design and analysis, potentially leading to significant advancements in computational complexity.

DOI: 10.5281/zenodo.22266756

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