论轨道词问题的复杂性

IF 1.8 2区数学 Q1 MATHEMATICS

Journal of Complexity Pub Date : 2025-01-16 DOI:10.1016/j.jco.2025.101929

Michael Maller

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引用次数: 0

摘要

在以前的工作中，我们定义了一个在二维环面微分同态动力学中出现的计算鞍转移问题，并证明了这个问题是在Oracle NP中，在一个适用于图灵机计算实数问题的计算模型中工作的。在这篇文章中，我们报告了对这些问题的进一步研究，研究了在周期点上用有限词表示的轨道描述。我们在Oracle NP模型中展示了这些轨道词问题。我们的方法还揭示了已实现轨道词集中的结构，为复杂性的进一步应用提供了建议。

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On the complexity of orbit word problems

In previous work we defined a computational saddle transition problem which arises in the dynamics of diffeomorphisms of the 2−dimensional torus, and proved this problem is in Oracle NP, working in a model of computation appropriate for Turing machine computations on problems defined over the real numbers. In this note we report further work on these problems, studying orbit descriptions represented as finite words in periodic points. We show these Orbit Word Problems are again in Oracle NP, in our model. Our methods also reveal structures in the set of realized orbit words, suggesting further applications in complexity.

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来源期刊

Journal of Complexity 工程技术-计算机：理论方法

CiteScore

3.10

自引率

17.60%

发文量

审稿时长

>12 weeks

期刊介绍： The multidisciplinary Journal of Complexity publishes original research papers that contain substantial mathematical results on complexity as broadly conceived. Outstanding review papers will also be published. In the area of computational complexity, the focus is on complexity over the reals, with the emphasis on lower bounds and optimal algorithms. The Journal of Complexity also publishes articles that provide major new algorithms or make important progress on upper bounds. Other models of computation, such as the Turing machine model, are also of interest. Computational complexity results in a wide variety of areas are solicited. Areas Include: • Approximation theory • Biomedical computing • Compressed computing and sensing • Computational finance • Computational number theory • Computational stochastics • Control theory • Cryptography • Design of experiments • Differential equations • Discrete problems • Distributed and parallel computation • High and infinite-dimensional problems • Information-based complexity • Inverse and ill-posed problems • Machine learning • Markov chain Monte Carlo • Monte Carlo and quasi-Monte Carlo • Multivariate integration and approximation • Noisy data • Nonlinear and algebraic equations • Numerical analysis • Operator equations • Optimization • Quantum computing • Scientific computation • Tractability of multivariate problems • Vision and image understanding.