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A Non-Orthogonal Modulation Based High Spectral Efficiency and High Security Multi-Carrier Differential Chaos Shift Keying for Maritime Communications 一种基于非正交调制的高频谱效率和高安全性的多载波差分混沌移位键控
IF 6.6 1区 计算机科学 Q1 Multidisciplinary Pub Date : 2024-06-26 DOI: 10.26599/TST.2024.9010057
Xinyu Dou;Tengxiao Lyu;Xiaohan Ren;Dequn Liang
The Space-Air-Ground-Sea Integrated Networks (SAGSIN) will place higher requirements on both spectral efficiency and security for future maritime communications. To simultaneously address these two challenges, in this paper, a non-orthogonal modulation based multi-carrier differential chaos shift keying system (namely MCNO-DCSK) is proposed and demonstrated. The most remarkable feature of MCNO-DCSK is that the strict orthogonality between subcarriers is no longer required. In this way, frequency intervals between subcarriers can be much smaller than ever, which leads to a high spectral efficiency. Meanwhile, the frequency interval can be set more flexibly to make the symbol more difficult to be deciphered. Therefore, a high level of security can also be guaranteed. In this design, multiple modulated non-orthogonal subcarriers are sequentially delayed and directly superimposed in time domain to construct the MCNO-DCSK symbol. At the receiver, information bits are demodulated through solving a system of linear equations. The spectral efficiency, computational complexity, and security are analyzed, and the bit-error-rate expressions are derived. Moreover, as subcarriers are non-orthogonal and time delayed, the MCNO-DCSK will suffer severe interference over the multi-path channel. Therefore, the effect of the multi-path interference on the system performance is discussed, and a method to mitigate this interference is designed. Finally, simulation results are provided to verify the theoretical analysis and demonstrate the superiority of MCNO-DCSK.
天空地海综合网络(SAGSIN)将对未来海上通信的频谱效率和安全性提出更高的要求。为了同时解决这两个挑战,本文提出并演示了一种基于非正交调制的多载波差分混沌移位键控系统(即MCNO-DCSK)。MCNO-DCSK最显著的特点是不再需要子载波之间的严格正交性。通过这种方式,子载波之间的频率间隔可以比以往小得多,从而导致高频谱效率。同时,可以更灵活地设置频率间隔,使符号更难被破译。因此,也可以保证高水平的安全性。在该设计中,多个调制的非正交子载波被顺序延迟并在时域上直接叠加以构造MCNO-DCSK符号。在接收端,通过求解一个线性方程组来解调信息位。分析了频谱效率、计算复杂度和安全性,推导了误码率表达式。此外,由于子载波是非正交的和时间延迟的,MCNO-DCSK将在多径信道上遭受严重的干扰。因此,本文讨论了多径干扰对系统性能的影响,并设计了一种抑制多径干扰的方法。最后给出了仿真结果,验证了理论分析和MCNO-DCSK的优越性。
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引用次数: 0
Joint Task Offloading and Resource Allocation Strategy for Space-Air-Ground Integrated Vehicular Networks 天空地一体化车载网络联合任务卸载与资源分配策略
IF 6.6 1区 计算机科学 Q1 Multidisciplinary Pub Date : 2024-06-26 DOI: 10.26599/TST.2024.9010055
Yuanshuo Gang;Yuexia Zhang;Zhihai Zhuo
Space-Air-Ground integrated Vehicular Network (SAGVN) aims to achieve ubiquitous connectivity and provide abundant computational resources to enhance the performance and efficiency of the vehicular networks. Nonetheless, there are still challenges to overcome, including the scheduling of multilayered computational resources and the scarcity of spectrum resources. To address these problems, we propose a joint Task Offloading (TO) and Resource Allocation (RA) strategy in SAGVN (namely JTRSS). This strategy establishes an SAGVN model that incorporates air and space networks to expand the options for vehicular TO, and enhances the edge-computing resources of the system by deploying edge servers. To minimize the system average cost, we use the JTRSS algorithm to decompose the original problem into a number of subproblems. A maximum rate matching algorithm is used to address the channel allocation and the Lagrangian multiplier method is employed for computational RA. To acquire the optimal TO decision, a differential fusion cuckoo search algorithm is designed. Extensive simulation results demonstrate the significant superiority of the JTRSS algorithm in optimizing the system average cost.
天空地一体化车载网络(SAGVN)旨在实现无所不在的连接,并提供丰富的计算资源,以提高车载网络的性能和效率。尽管如此,仍有许多挑战需要克服,包括多层计算资源的调度和频谱资源的稀缺性。为了解决这些问题,我们提出了在SAGVN(即JTRSS)中联合任务卸载(To)和资源分配(RA)策略。该策略建立了一个SAGVN模型,该模型结合了空中和空间网络,以扩展车载to的选择,并通过部署边缘服务器增强系统的边缘计算资源。为了使系统平均成本最小化,我们使用JTRSS算法将原始问题分解为许多子问题。采用最大速率匹配算法解决信道分配问题,采用拉格朗日乘子法计算RA。为了获得最优To决策,设计了一种差分融合布谷鸟搜索算法。大量的仿真结果表明,JTRSS算法在优化系统平均成本方面具有显著的优越性。
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引用次数: 0
Maximizing Overall Service Profit: Multi-Edge Service Pricing as a Stochastic Game Model 整体服务利润最大化:作为随机博弈模型的多边缘服务定价
IF 6.6 1区 计算机科学 Q1 Multidisciplinary Pub Date : 2024-06-20 DOI: 10.26599/TST.2024.9010050
Shengye Pang;Xinkui Zhao;Jiayin Luo;Jintao Chen;Fan Wang;Jianwei Yin
The diversified development of the service ecosystem, particularly the rapid growth of services like cloud and edge computing, has propelled the flourishing expansion of the service trading market. However, in the absence of appropriate pricing guidance, service providers often devise pricing strategies solely based on their own interests, potentially hindering the maximization of overall market profits. This challenge is even more severe in edge computing scenarios, as different edge service providers are dispersed across various regions and influenced by multiple factors, making it challenging to establish a unified pricing model. This paper introduces a multi-participant stochastic game model to formalize the pricing problem of multiple edge services. Subsequently, an incentive mechanism based on Pareto improvement is proposed to drive the game towards Pareto optimal direction, achieving optimal profits. Finally, an enhanced PSO algorithm was proposed by adaptively optimizing inertia factor across three stages. This optimization significantly improved the efficiency of solving the game model and analyzed equilibrium states under various evolutionary mechanisms. Experimental results demonstrate that the proposed pricing incentive mechanism promotes more effective and rational pricing allocations, while also demonstrating the effectiveness of our algorithm in resolving game problems.
服务生态系统的多元化发展,尤其是云计算和边缘计算等服务的快速增长,推动了服务交易市场的蓬勃发展。然而,在缺乏适当定价指导的情况下,服务提供商往往仅从自身利益出发制定定价策略,从而有可能阻碍市场整体利益的最大化。在边缘计算场景中,这一挑战更为严峻,因为不同的边缘服务提供商分散在不同地区,并受到多种因素的影响,因此建立统一的定价模型极具挑战性。本文介绍了一种多参与者随机博弈模型,将多种边缘服务的定价问题形式化。随后,提出了基于帕累托改进的激励机制,以推动博弈向帕累托最优方向发展,实现最优利润。最后,通过对三个阶段的惯性因子进行自适应优化,提出了一种增强型 PSO 算法。这种优化大大提高了博弈模型的求解效率,并分析了各种进化机制下的均衡状态。实验结果表明,所提出的定价激励机制促进了更有效、更合理的定价分配,同时也证明了我们的算法在解决博弈问题方面的有效性。
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引用次数: 0
On Time-Aware Cross-Blockchain Data Migration 关于时间感知的跨区块链数据迁移
IF 6.6 1区 计算机科学 Q1 Multidisciplinary Pub Date : 2024-06-20 DOI: 10.26599/TST.2023.9010136
Mengqiu Zhang;Qiang Qu;Li Ning;Jianping Fan
With the widespread adoption of blockchain applications, the imperative for seamless data migration among decentralized applications has intensified. This necessity arises from various factors, including the depletion of blockchain disk space, transitions between blockchain systems, and specific requirements such as temporal data analysis. To meet these challenges and ensure the sustained functionality of applications, it is imperative to conduct time-aware cross-blockchain data migration. This process is designed to facilitate the smooth iteration of decentralized applications and the construction of a temporal index for historical data, all while preserving the integrity of the original data. In various application scenarios, this migration task may encompass the transfer of data between multiple blockchains, involving movements from one chain to another, from one chain to several chains, or from multiple chains to a single chain. However, the success of data migration hinges on the careful consideration of factors such as the reliability of the data source, data consistency, and migration efficiency. This paper introduces a time-aware cross-blockchain data migration approach tailored to accommodate diverse application scenarios, including migration between multiple chains. The proposed solution integrates a collective mechanism for controlling, executing, and storing procedures to address the complexities of data migration, incorporating elements such as transaction classification and matching. Extensive experiments have been conducted to validate the efficacy of the proposed approach.
随着区块链应用的广泛采用,去中心化应用之间的无缝数据迁移变得更加迫切。产生这种必要性的因素有很多,包括区块链磁盘空间的耗尽、区块链系统之间的转换以及时间数据分析等特定要求。为了应对这些挑战并确保应用程序的持续功能,必须进行时间感知的跨区块链数据迁移。这一过程旨在促进去中心化应用的顺利迭代,并为历史数据构建时序索引,同时保持原始数据的完整性。在各种应用场景中,这种迁移任务可能包括在多个区块链之间传输数据,涉及从一个链到另一个链、从一个链到多个链或从多个链到一个链的移动。然而,数据迁移的成功取决于对数据源可靠性、数据一致性和迁移效率等因素的仔细考虑。本文介绍了一种时间感知的跨区块链数据迁移方法,该方法是为适应不同应用场景(包括多链之间的迁移)而量身定制的。所提出的解决方案整合了一种用于控制、执行和存储程序的集体机制,以解决数据迁移的复杂性问题,并纳入了交易分类和匹配等要素。为验证所提方法的有效性,我们进行了广泛的实验。
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引用次数: 0
Enhancing Power Line Insulator Health Monitoring with a Hybrid Generative Adversarial Network and YOLO3 Solution 利用混合生成式对抗网络和 YOLO3 解决方案加强电力线绝缘体健康监测
IF 6.6 1区 计算机科学 Q1 Multidisciplinary Pub Date : 2024-06-20 DOI: 10.26599/TST.2023.9010137
Ramakrishna Akella;Sravan Kumar Gunturi;Dipu Sarkar
In the critical field of electrical grid maintenance, ensuring the integrity of power line insulators is a primary concern. This study introduces an innovative approach for monitoring the condition of insulators using aerial surveillance via drone-mounted cameras. The proposed method is a composite deep learning framework that integrates the “You Only Look Once” version 3 (YOLO3) model with deep convolutional generative adversarial networks (DCGAN) and super-resolution generative adversarial networks (SRGAN). The YOLO3 model excels in rapidly and accurately detecting insulators, a vital step in assessing their health. Its effectiveness in distinguishing insulators against complex backgrounds enables prompt detection of defects, essential for proactive maintenance. This rapid detection is enhanced by DCGAN's precise classification and SRGAN's image quality improvement, addressing challenges posed by low-resolution drone imagery. The framework's performance was evaluated using metrics such as sensitivity, specificity, accuracy, localization accuracy, damage sensitivity, and false alarm rate. Results show that the SRGAN+DCGAN+YOLO3 model significantly outperforms existing methods, with a sensitivity of 98%, specificity of 94%, an overall accuracy of 95.6%, localization accuracy of 90%, damage sensitivity of 92%, and a reduced false alarm rate of 8%. This advanced hybrid approach not only improves the detection and classification of insulator conditions but also contributes substantially to the maintenance and health of power line insulators, thus ensuring the reliability of the electrical power grid.
在电网维护这一关键领域,确保电力线路绝缘子的完整性是首要问题。本研究介绍了一种利用无人机安装的摄像头进行空中监控来监测绝缘子状况的创新方法。所提出的方法是一种复合深度学习框架,它将 "你只看一次 "第三版(YOLO3)模型与深度卷积生成对抗网络(DCGAN)和超分辨率生成对抗网络(SRGAN)集成在一起。YOLO3 模型在快速准确地检测绝缘体方面表现出色,这是评估绝缘体健康状况的重要一步。该模型能有效区分复杂背景下的绝缘子,从而及时发现缺陷,这对主动维护至关重要。DCGAN 的精确分类和 SRGAN 的图像质量改进增强了这种快速检测能力,解决了低分辨率无人机图像带来的挑战。使用灵敏度、特异性、准确性、定位精度、损坏灵敏度和误报率等指标对该框架的性能进行了评估。结果表明,SRGAN+DCGAN+YOLO3 模型明显优于现有方法,灵敏度为 98%,特异性为 94%,总体准确率为 95.6%,定位准确率为 90%,损坏灵敏度为 92%,误报率降低了 8%。这种先进的混合方法不仅提高了绝缘体状态的检测和分类能力,而且大大有助于维护电力线路绝缘体的健康,从而确保电网的可靠性。
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引用次数: 0
Streaming Histogram Publication Over Weighted Sliding Windows Under Differential Privacy 在差异隐私条件下通过加权滑动窗口进行流式直方图发布
IF 6.6 1区 计算机科学 Q1 Multidisciplinary Pub Date : 2024-06-20 DOI: 10.26599/TST.2023.9010083
Xiujun Wang;Lei Mo;Xiao Zheng;Zhe Dang
Continuously publishing histograms in data streams is crucial to many real-time applications, as it provides not only critical statistical information, but also reduces privacy leaking risk. As the importance of elements usually decreases over time in data streams, in this paper we model a data stream by a sequence of weighted sliding windows, and then study how to publish histograms over these windows continuously. The existing literature can hardly solve this problem in a real-time way, because they need to buffer all elements in each sliding window, resulting in high computational overhead and prohibitive storage burden. In this paper, we overcome this drawback by proposing an online algorithm denoted by Efficient Streaming Histogram Publishing (ESHP) to continuously publish histograms over weighted sliding windows. Specifically, our method first creates a novel sketching structure, called Approximate-Estimate Sketch (AESketch), to maintain the counting information of each histogram interval at every time instance; then, it creates histograms that satisfy the differential privacy requirement by smartly adding appropriate noise values into the sketching structure. Extensive experimental results and rigorous theoretical analysis demonstrate that the ESHP method can offer equivalent data utility with significantly lower computational overhead and storage costs when compared to other existing methods.
在数据流中持续发布直方图对许多实时应用至关重要,因为它不仅能提供关键的统计信息,还能降低隐私泄露风险。在数据流中,元素的重要性通常会随着时间的推移而降低,因此我们在本文中用一系列加权滑动窗口来模拟数据流,然后研究如何在这些窗口上连续发布直方图。现有文献很难实时解决这个问题,因为它们需要缓冲每个滑动窗口中的所有元素,从而导致高计算开销和令人望而却步的存储负担。在本文中,我们提出了一种名为 "高效流直方图发布"(ESHP)的在线算法,通过加权滑动窗口连续发布直方图,从而克服了这一缺点。具体来说,我们的方法首先创建了一种名为 "近似估计草图(AESketch)"的新颖草图结构,以保持每个时间实例中每个直方图区间的计数信息;然后,通过在草图结构中巧妙地添加适当的噪声值,创建满足差分隐私要求的直方图。广泛的实验结果和严谨的理论分析表明,与其他现有方法相比,ESHP 方法能以更低的计算开销和存储成本提供同等的数据效用。
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引用次数: 0
Total Contents 总内容
IF 6.6 1区 计算机科学 Q1 Multidisciplinary Pub Date : 2024-06-20
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引用次数: 0
Effective Application of IoT Power Electronics Technology and Power System Optimization Control 物联网电力电子技术的有效应用与电力系统的优化控制
IF 6.6 1区 计算机科学 Q1 Multidisciplinary Pub Date : 2024-06-20 DOI: 10.26599/TST.2023.9010124
Libo Yang;Bin Ma;Long Yuan;Bingxiang Wu
With the development of society, the power system plays an important role in the global energy structure. However, facing increasing energy demand and environmental pressure, improving power system efficiency, reducing costs, and ensuring reliability and safety have become key issues. The Internet of Things (IoT) power electronics technology, as one of the research hotspots, integrates IoT and power electronics technology to achieve intelligent and optimized control of power systems through sensors, communication, and control technologies. In order to meet current and future needs, it is necessary to optimize the operation and management of power systems using IoT power electronics technology. By analyzing the application of Internet of Things power electronics technology and the optimal dispatch of power systems, support vector machine algorithms are used to analyze and process equipment data, and perform data monitoring and anomaly detection to promote energy waste reduction and energy saving, and then start from operation and maintenance respectively. Comparative simulation experiments were conducted in five aspects: efficiency, effectiveness of power load prediction and optimization control, effectiveness of intelligent monitoring, operating costs, and data security. The experimental results show that the operation and maintenance efficiency of the power system using IoT power electronics technology has been improved to only 18 h for equipment fault handling. The accuracy of load forecasting optimization control based on IoT power electronics technology reaches 94%. The fault detection accuracy of intelligent monitoring of power equipment based on the power electronics technology of the Internet of Things has reached 96%. At the same time, the Internet of Things power electronics technology was used to improve the power operation mode, so as to promote the monthly electricity sales revenue of 2.77 million RMB. In addition, the effectiveness of IoT power electronics technology in power data security management has reached 95%. In summary, IoT power electronics technology can improve the stability, reliability, and security of power systems, reduce costs, improve efficiency and management level, and has broad application and promotion prospects.
随着社会的发展,电力系统在全球能源结构中扮演着重要角色。然而,面对日益增长的能源需求和环境压力,提高电力系统效率、降低成本、确保可靠性和安全性已成为关键问题。物联网电力电子技术作为研究热点之一,将物联网与电力电子技术相结合,通过传感器、通信和控制技术实现电力系统的智能优化控制。为了满足当前和未来的需求,有必要利用物联网电力电子技术优化电力系统的运行和管理。通过分析物联网电力电子技术的应用和电力系统的优化调度,利用支持向量机算法对设备数据进行分析和处理,并进行数据监测和异常检测,促进能源浪费的减少和节能,然后分别从运行和维护两方面入手。从效率、电力负荷预测和优化控制效果、智能监控效果、运行成本和数据安全五个方面进行了对比模拟实验。实验结果表明,采用物联网电力电子技术的电力系统运维效率提高,设备故障处理仅需 18 小时。基于物联网电力电子技术的负荷预测优化控制精度达到94%。基于物联网电力电子技术的电力设备智能监控的故障检测准确率达到 96%。同时,利用物联网电力电子技术改进电力运行方式,促进每月售电收入 277 万元。此外,物联网电力电子技术在电力数据安全管理方面的有效性也达到了 95%。综上所述,物联网电力电子技术可以提高电力系统的稳定性、可靠性和安全性,降低成本,提高效率和管理水平,具有广阔的应用和推广前景。
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引用次数: 0
ZKP Protocols for Usowan, Herugolf, and Five Cells 乌索万、赫鲁戈夫和五细胞的 ZKP 协议
IF 6.6 1区 计算机科学 Q1 Multidisciplinary Pub Date : 2024-06-20 DOI: 10.26599/TST.2023.9010153
Daiki Miyahara;Léo Robert;Pascal Lafourcade;Takaaki Mizuki
A Zero-Knowledge Proof (ZKP) protocol allows a participant to prove the knowledge of some secret without revealing any information about it. While such protocols are typically executed by computers, there exists a line of research proposing physical instances of ZKP protocols. Up to now, many card-based ZKP protocols for pen-and-pencil puzzles, like Sudoku, have been designed. Those games, mostly edited by Nikoli, have simple rules, yet designing them in card-based ZKP protocols is non-trivial. In this work, we propose a card-based ZKP protocol for Usowan, a Nikoli game. In Usowan, for each room of a puzzle instance, there is exactly one piece of false information. The goal of the game is to detect this wrong data amongst the correct data and also to satisfy the other rules. Designing a card-based ZKP protocol to deal with the property of detecting a liar has never been done. In some sense, we propose a physical ZKP for hiding of a liar. This work extends a previous paper appearing in Ref. [1]. In this extension, we propose two other protocols, for Herugolf and Five Cells. The puzzles are specifically chosen because each of those three puzzles shares a common constraint, connectivity. However, showing the connected configuration cannot be done with generic approach and brings new construction to the existing connectivity ZKP protocol. Indeed, in Herugolf, the connectivity is handled with a given length of cell which is decremental (i.e., the length of each connected cell decreases by one at each step). For Five Cells, there is an additional step in the setup allowing to encode all the information needed to ensure a valid ZKP protocol.
零知识证明(ZKP)协议允许参与者在不透露任何相关信息的情况下证明对某个秘密的了解。虽然此类协议通常由计算机执行,但也有一系列研究提出了 ZKP 协议的物理实例。迄今为止,人们已经设计出许多基于卡片的 ZKP 协议,用于数独等纸笔谜题。这些游戏大多由 Nikoli 编辑,规则简单,但要将其设计成基于卡片的 ZKP 协议却并非易事。在这项工作中,我们为尼科利游戏 "乌索万"(Usowan)提出了一种基于卡片的 ZKP 协议。在 "乌索万 "游戏中,每个谜题实例的每个房间都有一条虚假信息。游戏的目标是在正确的数据中检测出这些错误的数据,并满足其他规则的要求。设计一个基于卡片的 ZKP 协议来处理检测骗子的属性,还从未有人做过。从某种意义上说,我们提出了一种用于隐藏骗子的物理 ZKP。这项工作扩展了参考文献 [1] 中的一篇论文。[1].在这一扩展中,我们提出了另外两个协议:Herugolf 和 Five Cells。之所以特别选择这两个谜题,是因为这三个谜题都有一个共同的约束条件--连通性。然而,显示连通性配置无法用通用方法完成,这就给现有的连通性 ZKP 协议带来了新的构造。事实上,在 Herugolf 中,连通性是通过给定的单元长度来处理的,而单元长度是递减的(即每个连通单元的长度每一步都递减一个)。对于 "五单元",在设置过程中还有一个额外的步骤,可以对所有必要的信息进行编码,以确保 ZKP 协议的有效性。
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引用次数: 0
On Concept Lattices for Numberings 论编号的概念网格
IF 6.6 1区 计算机科学 Q1 Multidisciplinary Pub Date : 2024-06-20 DOI: 10.26599/TST.2023.9010102
Nikolay Bazhenov;Manat Mustafa;Anvar Nurakunov
The theory of numberings studies uniform computations for families of mathematical objects. In this area, computability-theoretic properties of at most countable families of sets $mathcal{S}$ are typically classified via the corresponding Rogers upper semilattices. In most cases, a Rogers semilattice cannot be a lattice. Working within the framework of Formal Concept Analysis, we develop two new approaches to the classification of families $mathcal{S}$. Similarly to the classical theory of numberings, each of the approaches assigns to a family $mathcal{S}$ its own concept lattice. The first approach captures the cardinality of a family $mathcal{S}$: if $mathcal{S}$ contains more than 2 elements, then the corresponding concept lattice FC1($mathcal{S}$) is a modular lattice of height 3, such that the number of its atoms to the cardinality of $mathcal{S}$. Our second approach gives a much richer environment. We prove that for any countable poset $P$, there exists a family $mathcal{S}$ such that the induced concept lattice FC2 ($mathcal{S}$) is isomorphic to the Dedekind-MacNeille completion of $P$. We also establish connections with the class of enumerative lattices introduced by Hoyrup and Rojas in their studies of algorithmic randomness. We show that every lattice FC2 ($mathcal{S}$) is anti-isomorphic to an enumerative lattice. In addition, every enumerative lattice is anti-isomorphic to a sublattice of the lattice FC2 ($mathcal{S}$) for some family $mathcal{S}$.
数集理论研究数学对象族的统一计算。在这一领域,集合 $mathcal{S}$ 的最可数族的可计算性理论性质通常是通过相应的罗杰斯上半格来分类的。在大多数情况下,罗杰斯半格不可能是格。在形式概念分析的框架内,我们开发了两种新方法来对$mathcal{S}$族进行分类。与经典的编号理论类似,每一种方法都为$mathcal{S}$族分配了自己的概念网格。第一种方法捕捉到了$mathcal{S}$族的万有引力:如果$mathcal{S}$包含2个以上的元素,那么相应的概念网格FC1($mathcal{S}$)就是一个高度为3的模块网格,这样它的原子数就等于$mathcal{S}$的万有引力。我们的第二种方法提供了更丰富的环境。我们证明,对于任何可数正集 $P$,都存在一个族 $/mathcal{S}$,使得诱导概念网格 FC2 ($mathcal{S}$) 与 $P$ 的戴德金-麦克尼尔补全同构。我们还建立了与霍伊鲁普和罗哈斯在算法随机性研究中引入的枚举网格类的联系。我们证明了每个网格 FC2 ($mathcal{S}$) 都与枚举网格反同构。此外,对于某个族 $mathcal{S}$,每个枚举网格都与网格 FC2 ($mathcal{S}$) 的子网格反同构。
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引用次数: 0
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Tsinghua Science and Technology
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