Negative results on density determination with one-dimensional cellular automata with block-sequential asynchronous updates

IF 3.1 3区计算机科学 Q2 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Journal of Computational Science Pub Date : 2024-09-02 DOI:10.1016/j.jocs.2024.102430

Eurico Ruivo , Kévin Perrot , Pedro Paulo Balbi , Pacôme Perrotin

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引用次数: 0

Abstract

A large number of research efforts have been made in trying to solve global decision problems with cellular automata by means of their cells reaching a distributed consensus via their local action. Among them, the determination of the most frequent state in configurations with arbitrary size, i.e., the density classification task, has been the most widely approached benchmark problem. The literature abounds with cases demonstrating that, depending on how it is formulated, a solution can be shown to exist or not. Here we address the problem in terms of deterministic, block-sequential asynchronous updates, over cyclic configurations, by which the possibility of a solution remains open. Our main results are negative in terms of the possibility of solving the problem with such formulation, encompassing the cases of any cellular automaton with any sequential update, and any elementary cellular automaton with any block-sequential update; furthermore, we uncover some properties that any potential solution with block-sequential update should have in order for it to be a candidate to solving the problem. Incidentally, we also give a new, very simple proof of the impossibility of solving the problem with any synchronous rule.

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用分块序列异步更新的一维蜂窝自动机确定密度的负面结果

人们已经做了大量研究工作，试图通过细胞的局部行动达成分布式共识，从而用细胞自动机解决全局决策问题。其中，在任意大小的配置中确定最常出现的状态，即密度分类任务，一直是研究最为广泛的基准问题。文献中大量案例表明，根据问题的表述方式，可以证明解决方案存在与否。在这里，我们从循环配置的确定性、块序列异步更新的角度来解决这个问题，通过这种方式，解决方案的可能性仍然是开放的。我们的主要结果否定了用这种方法解决问题的可能性，包括任何具有顺序更新的蜂窝自动机和任何具有分块顺序更新的基本蜂窝自动机的情况；此外，我们还发现了任何具有分块顺序更新的潜在解决方案应具备的一些特性，以便使其成为解决问题的候选方案。顺便提一下，我们还给出了一个新的、非常简单的证明，证明不可能用任何同步规则来解决这个问题。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Computational Science COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS-COMPUTER SCIENCE, THEORY & METHODS

CiteScore

5.50

自引率

3.00%

发文量

227

审稿时长

41 days

期刊介绍： Computational Science is a rapidly growing multi- and interdisciplinary field that uses advanced computing and data analysis to understand and solve complex problems. It has reached a level of predictive capability that now firmly complements the traditional pillars of experimentation and theory. The recent advances in experimental techniques such as detectors, on-line sensor networks and high-resolution imaging techniques, have opened up new windows into physical and biological processes at many levels of detail. The resulting data explosion allows for detailed data driven modeling and simulation. This new discipline in science combines computational thinking, modern computational methods, devices and collateral technologies to address problems far beyond the scope of traditional numerical methods. Computational science typically unifies three distinct elements: • Modeling, Algorithms and Simulations (e.g. numerical and non-numerical, discrete and continuous); • Software developed to solve science (e.g., biological, physical, and social), engineering, medicine, and humanities problems; • Computer and information science that develops and optimizes the advanced system hardware, software, networking, and data management components (e.g. problem solving environments).