[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-124161-en":3,"doc-seo-124161-105":29,"detail-sidebar-cat-0-en-105":89},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":4,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":20,"language":21,"language_code":22,"site_id":23,"html_lang":22,"table_of_contents":24,"faqs":25,"seo_title":26,"seo_description":14,"update_tm":27,"read_time":28},124161,13056703019404,"Miles","https://ap-avatar.wpscdn.com/davatar_29158cc5080c5b710cf443261637dec0",6,"Technology","Learning to Flash - A Machine Learning Approach to Synchronizing Cellular Automata","Cellular automata (CA) are discrete dynamical systems whose simple local interactions can produce complex global behavior. This work studies global synchronization in a one-dimensional stochastic CA, where cells evolve into a homogeneous blinking state. A data-driven method based on deep learning is introduced to infer probabilistic cellular automaton rules that learn the synchronization task. The approach reframes known CA difficulties through an exploratory perspective and enables analysis of synchronization time and its relation to deterministic cases.","2023 International Symposium on Nonlinear Theory and Its Applications NOLTA2023, September 26-29, 2023, Catania and Online  \nLearning to Flash: A Machine Learning Approach to Synchronizing Cellular  \nAutomata  \nMartin Schueley  \nyInstitute of Computational Life Sciences, Zurich University of Applied Sciences  \nSwitzerland  \nmartin.schuele@zhaw.ch  \nAbstract􀂗 Cellular automata (CA) are discrete dynamical systems of cells with simple local interaction mechanisms that can exhibit surprisingly complex behaviour. Due to the local interaction, it is well known that certain global properties of the system are di􀀎cult to control. In this paper, we investigate one such global behaviour, namely the possibility of synchronisation of the cells of a one-dimensional stochastic CA, and how this can be achieved by an approach that uses machine learning. The approach allows us to tackle well-known problems in CA theories from anew, exploratory perspective.  \n1. Introduction  \nThe synchronization problem involves 􀀂nding a cellular automaton (CA) that can evolve any initial condition into a homogeneous blinking state for one-dimensional binary systems with periodic boundary conditions. Deterministic solutions to this problem are elusive, but incorporating randomness in the local rules permits stochastic solutions.  \nThe main question this contribution aims to address is whether a probabilistic CA (PCA) can learn to solve the synchronization problem independently, by developing an approach based on deep learning techniques.  \n2. Probabilistic CA and the Synchronization Problem  \nA CA is a discrete dynamical system where cells on a lattice change states based on neighboring cell states [1] . With PCA, cell states are updated using local probability transition functions.  \nA CA is considered to have solved the global synchronization problem if it reaches a 􀂔blinking state􀂔, which means that it alternates between two homogeneous con􀀂gurations from any initial condition (as shown in Figure 1) . It is known that a deterministic solution does not exist for the CA synchronization problem. However, if some randomness is introduced in the local rules, stochastic solutions can be achieved easily [2] . The time which it takes to reach the blinking state is however also subject to investigation.  \nORCID iDs First Author: 0000-0002-9379-4887  \nFigure 1: Space-time diagrams of CA. Time goes from bottom to top, white and blue squares represent cells in state 0 and 1, respectively. For (a)-(c) the CA synchronizes, whereas in (d) it does not. Figure from [2] .  \n3. Learning PCA Rules  \nInspired by the deep learning methodology, we propose a data-driven approach to infer rules for solving the synchronization problem using PCA. Training data can be gathered by collecting sets of labeled initial con􀀂gurations depending on their synchronization potential. Viewing PCA as aspeci􀀂c type of neural network, the output is a probability distribution over con􀀂gurations obtained from the probabilistic transition table.  \nBy comparing the network output with target distributions through a loss function, we can learn parameters that minimize the loss using a gradient descent algorithm. These parameters can specify the probabilistic transition rule needed to solve the synchronization problem. It also allows to investigate further the mean time of synchronization and the relationship to the deterministic case. Note that the approach is demonstrated in the context of the synchronization problem, but can also be applied to other related problems.  \nReferences  \n[1] J. Kari, 􀂓Theory of cellular automata: A survey􀂔, Theoretical Computer Science 334.1-3: 3-33, 2005 .  \n[2] N. Fates, 􀂓Remarks on the cellular automaton global synchronisation problem􀂔, International Workshop on Cellular Automata and Discrete Complex Systems, 2015.  \nThis work is licensed under a Creative Commons  \nAttribution-NonCommercial-NoDerivatives 4.0 International.","cbCairzugpKeHLdU","https://ap.wps.com/l/cbCairzugpKeHLdU","pdf",383199,1,"English","en",105,"# Abstract\n# Introduction\n# Probabilistic CA and the Synchronization Problem\n# Learning PCA Rules\n# References","[{\"question\":\"What problem does the paper focus on regarding cellular automata?\",\"answer\":\"It focuses on whether a probabilistic cellular automaton can learn to synchronize, driving any initial condition toward a homogeneous blinking state in one-dimensional binary systems with periodic boundary conditions.\"},{\"question\":\"Why are stochastic rules important for synchronization in this context?\",\"answer\":\"Deterministic solutions are described as elusive, while introducing randomness into local rules enables stochastic solutions that can achieve the blinking state.\"},{\"question\":\"How does the proposed method learn synchronization behavior?\",\"answer\":\"It treats the probabilistic CA as a neural-network-like model, learns parameters by minimizing a loss function between network outputs and target distributions, and thereby infers probabilistic transition rules for synchronization.\"}]","Learning to Flash - A Machine Learning Approach to Synchronizing Cellular Automata | PDF",1785820803,3,{"code":4,"msg":30,"data":31},"ok",{"site_id":23,"language":22,"slug":32,"title":13,"keywords":33,"description":14,"schema_data":34,"social_meta":84,"head_meta":86,"extra_data":88,"updated_unix":27},"learning-to-flash-a-machine-learning-approach-to-synchronizing-cellular-automata","",{"@graph":35,"@context":83},[36,52,66],{"@type":37,"itemListElement":38},"BreadcrumbList",[39,43,47,49],{"item":40,"name":41,"@type":42,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":44,"name":45,"@type":42,"position":46},"https://docshare.wps.com/document/","Document",2,{"item":48,"name":12,"@type":42,"position":28},"https://docshare.wps.com/document/technology/",{"item":50,"name":13,"@type":42,"position":51},"https://docshare.wps.com/document/learning-to-flash-a-machine-learning-approach-to-synchronizing-cellular-automata/124161/",4,{"url":50,"name":13,"@type":53,"author":54,"headline":13,"publisher":56,"fileFormat":59,"inLanguage":22,"description":14,"dateModified":60,"datePublished":60,"encodingFormat":59,"isAccessibleForFree":61,"interactionStatistic":62},"DigitalDocument",{"name":9,"@type":55},"Person",{"url":40,"name":57,"@type":58},"DocShare","Organization","application/pdf","2026-08-04",true,{"@type":63,"interactionType":64,"userInteractionCount":4},"InteractionCounter",{"@type":65},"ViewAction",{"@type":67,"mainEntity":68},"FAQPage",[69,75,79],{"name":70,"@type":71,"acceptedAnswer":72},"What problem does the paper focus on regarding cellular automata?","Question",{"text":73,"@type":74},"It focuses on whether a probabilistic cellular automaton can learn to synchronize, driving any initial condition toward a homogeneous blinking state in one-dimensional binary systems with periodic boundary conditions.","Answer",{"name":76,"@type":71,"acceptedAnswer":77},"Why are stochastic rules important for synchronization in this context?",{"text":78,"@type":74},"Deterministic solutions are described as elusive, while introducing randomness into local rules enables stochastic solutions that can achieve the blinking state.",{"name":80,"@type":71,"acceptedAnswer":81},"How does the proposed method learn synchronization behavior?",{"text":82,"@type":74},"It treats the probabilistic CA as a neural-network-like model, learns parameters by minimizing a loss function between network outputs and target distributions, and thereby infers probabilistic transition rules for synchronization.","https://schema.org",{"og:url":50,"og:type":85,"og:title":13,"og:site_name":57,"og:description":14},"article",{"robots":87,"canonical":50},"index,follow",{"doc_id":7,"site_id":23},{"code":4,"msg":5,"data":90},[91,95,99,103,108,111,116,121,126,129,133],{"id":20,"doc_module":4,"doc_module_name":45,"category_name":92,"show_sort_weight":93,"slug":94},"Story & Novel",90,"story-novel",{"id":46,"doc_module":4,"doc_module_name":45,"category_name":96,"show_sort_weight":97,"slug":98},"Literature",80,"literature",{"id":51,"doc_module":4,"doc_module_name":45,"category_name":100,"show_sort_weight":101,"slug":102},"Exam",70,"exam",{"id":104,"doc_module":4,"doc_module_name":45,"category_name":105,"show_sort_weight":106,"slug":107},5,"Comic",60,"comic",{"id":11,"doc_module":4,"doc_module_name":45,"category_name":12,"show_sort_weight":109,"slug":110},50,"technology",{"id":112,"doc_module":4,"doc_module_name":45,"category_name":113,"show_sort_weight":114,"slug":115},7,"Healthcare",40,"healthcare",{"id":117,"doc_module":4,"doc_module_name":45,"category_name":118,"show_sort_weight":119,"slug":120},8,"Research & Report",30,"research-report",{"id":122,"doc_module":4,"doc_module_name":45,"category_name":123,"show_sort_weight":124,"slug":125},9,"Religion & Spirituality",20,"religion-spirituality",{"id":124,"doc_module":4,"doc_module_name":45,"category_name":127,"show_sort_weight":124,"slug":128},"World Cup","world-cup",{"id":130,"doc_module":4,"doc_module_name":45,"category_name":131,"show_sort_weight":130,"slug":132},10,"Lifestyle","lifestyle",{"id":134,"doc_module":4,"doc_module_name":45,"category_name":135,"show_sort_weight":104,"slug":136},19,"General","general"]