Attractor Basins in Concurrent Systems

Attractor Basins in Concurrent Systems | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Attractor Basins in Concurrent Systems Giann Karlo Aguirre-Samboní, Stefan Haar, Loïc Paulevé, Stefan Schwoon, and 1 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7092034/v1 This work is licensed under a CC BY 4.0 License Status: Under Revision Version 1 posted 9 You are reading this latest preprint version Abstract A crucial question in analyzing a concurrent system is to determine its long-run behaviour, and in particular, whether there are irreversible choices in its evolution, leading into parts of the reachability space from which there is no return to other parts. Casting this problem in the unifying framework of safe Petri nets, we have provided in previous work techniques for identifying attractors, i.e. terminal strongly connected components of the reachability space. Here, what we aim at is to determine the attraction basins associated to those attractors; that is, those states from where all infinite runs are doomed to end in the given attractor, as opposed to those that are free to evolve differently. Here, we provide a solution for the case of safe Petri nets. Our algorithm uses net unfoldings and provides a map of all of those configurations (concurrent executions of the system) that lead onto cliff-edges, i.e. any maximal extension for those configurations lies in some basin that is considered fatal. safe Petri nets Unfoldings Attractor basins Multistability Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Revision Version 1 posted Editorial decision: Revision requested 19 Jan, 2026 Reviews received at journal 16 Jan, 2026 Reviews received at journal 28 Nov, 2025 Reviewers agreed at journal 02 Oct, 2025 Reviewers agreed at journal 19 Sep, 2025 Reviewers invited by journal 16 Sep, 2025 Editor assigned by journal 26 Aug, 2025 Submission checks completed at journal 12 Jul, 2025 First submitted to journal 10 Jul, 2025 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-7092034","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":517498455,"identity":"b524150d-bbfa-40c5-bf50-e290e1c526d2","order_by":0,"name":"Giann Karlo Aguirre-Samboní","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA3UlEQVRIiWNgGAWjYDACZhBxgIGBjb0ByDCwIEELH88BkBYJYq0CqpaTSACxiNAi78787HHBGTt7NsnnVzf8KJBg4G/vTsCrxfAwm7nxjBvJiW3SOWU3e4AOkzhzdgN+Lc0MZtI8H5gT2KRz0m7wALUYSOQS0sL+DailHuiwM2k3/xCjRZ6ZB2jLjcOMbRLsx24TZYsBM0+ZNM+Z44ltPDlst2UMJHgI+kW+//g2aZ5j1fby7cef3Xzzx0aOv72XgC0H4EweAzCJVznYlgY4k/0BQdWjYBSMglEwMgEA8lpBZE0lmMgAAAAASUVORK5CYII=","orcid":"","institution":"Mines Paris, PSL University","correspondingAuthor":true,"prefix":"","firstName":"Giann","middleName":"Karlo","lastName":"Aguirre-Samboní","suffix":""},{"id":517498456,"identity":"e177b04e-6d5d-494a-8b2d-4a32b2d8fee7","order_by":1,"name":"Stefan Haar","email":"","orcid":"","institution":"Inria Saclay - 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