Automated reasoning boosted by a probabilistic automaton classifier: An application to the Andrews-Curtis conjecture

Automated reasoning boosted by a probabilistic automaton classifier: An application to the Andrews-Curtis conjecture | 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 Automated reasoning boosted by a probabilistic automaton classifier: An application to the Andrews-Curtis conjecture Michael Fairbank, Alexei Lisitsa, Alexei Vernitski This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7157019/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 9 You are reading this latest preprint version Abstract Automated reasoning can take a prohibitively long time to run. We present a combined approach which makes automated reasoning more efficient by using supervised learning to identify promising tasks for automated reasoning. For supervised learning, we have developed a new, simple and efficient way of training an automaton classifier. We demonstrate the efficiency of our approach on examples drawn from the Andrews-Curtis conjecture, a famously challenging problem. Automated theorem proving supervised learning group theory Andrews–Curtis conjecture finite automaton Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Editorial decision: Revision requested 06 Oct, 2025 Reviews received at journal 01 Oct, 2025 Reviews received at journal 26 Sep, 2025 Reviewers agreed at journal 11 Aug, 2025 Reviewers agreed at journal 30 Jul, 2025 Reviewers invited by journal 29 Jul, 2025 Editor assigned by journal 22 Jul, 2025 Submission checks completed at journal 22 Jul, 2025 First submitted to journal 18 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-7157019","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":492774113,"identity":"a325f64e-0988-42cb-a156-0cb29653b745","order_by":0,"name":"Michael Fairbank","email":"","orcid":"","institution":"University of Essex","correspondingAuthor":false,"prefix":"","firstName":"Michael","middleName":"","lastName":"Fairbank","suffix":""},{"id":492774115,"identity":"1f7568ab-4b9a-42bc-8326-80425d7c3ffe","order_by":1,"name":"Alexei Lisitsa","email":"","orcid":"","institution":"University of Liverpool","correspondingAuthor":false,"prefix":"","firstName":"Alexei","middleName":"","lastName":"Lisitsa","suffix":""},{"id":492774116,"identity":"e03d2fa8-0f1b-4a47-a52f-389ba3e949ee","order_by":2,"name":"Alexei Vernitski","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAx0lEQVRIiWNgGAWjYPACGyQ2D3Fa0kjXcpgELfz9ZwwfV+44Lyfff/iYBEONHYPBmQP4tUjcyDE2PHvmtrHBjbRkA4ZjyQwGZxsIWHODLU2yse124gYJHsMHDGwHGAzOE9Ahf/5Y+s/GtnP18/vPfzjA8I8ILQYHko8xNrYdSGA4kMP4gLHtAGGHGd5IPgx0WLLhhhtpxgaJfck8koS8L3f+YOPHxjY7eWCIPZP48M1Oju9MAgGXoYAEoiNyFIyCUTAKRgFeAABi3kQ5nJHwxAAAAABJRU5ErkJggg==","orcid":"","institution":"University of Essex","correspondingAuthor":true,"prefix":"","firstName":"Alexei","middleName":"","lastName":"Vernitski","suffix":""}],"badges":[],"createdAt":"2025-07-18 11:08:15","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-7157019/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7157019/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":87906357,"identity":"9d73d5da-db66-4627-a931-2f2a1e4262bf","added_by":"auto","created_at":"2025-07-30 08:56:10","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":370857,"visible":true,"origin":"","legend":"","description":"","filename":"JARsubmit.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7157019/v1_covered_b629e2d7-12dd-467d-abd5-df82d8033a42.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Automated reasoning boosted by a probabilistic automaton classifier: An application to the Andrews-Curtis conjecture","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"journal-of-automated-reasoning","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"jars","sideBox":"Learn more about [Journal of Automated Reasoning](http://link.springer.com/journal/10817)","snPcode":"10817","submissionUrl":"https://submission.nature.com/new-submission/10817/3","title":"Journal of Automated Reasoning","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Automated theorem proving, supervised learning, group theory, Andrews–Curtis conjecture, finite automaton","lastPublishedDoi":"10.21203/rs.3.rs-7157019/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7157019/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"Automated reasoning can take a prohibitively long time to run. 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