How (not) to Compute the Halting Probability.

How (not) to Compute the Halting Probability. | 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 How (not) to Compute the Halting Probability. Manizheh Jalilvand, Behzad Nikzad, Saeed Salehi This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4015804/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract We study Chaitin’s well-known constant number Omega, and show that it is not a probability of halting the randomly chosen input-free programs. We suggest some methods for defining the halting probabilities by various measures. Mathematics Subject Classification (2020): 60A10 · 28A05 · 68Q04 · 03D10. Chaitin’s Constant The Omega Number Halting Probability Probability Measure Kolmogorov Axioms Algorithmic Information Theory. Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted 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. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. 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-4015804","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":278133486,"identity":"6a3d194c-56a9-4067-8d1d-81e0c64f7ac8","order_by":0,"name":"Manizheh Jalilvand","email":"","orcid":"","institution":"Shahid Beheshti University","correspondingAuthor":false,"prefix":"","firstName":"Manizheh","middleName":"","lastName":"Jalilvand","suffix":""},{"id":278133488,"identity":"14e6db24-0adf-40e3-8af1-134a67ea4f23","order_by":1,"name":"Behzad Nikzad","email":"","orcid":"","institution":"University of Tabriz","correspondingAuthor":false,"prefix":"","firstName":"Behzad","middleName":"","lastName":"Nikzad","suffix":""},{"id":278133490,"identity":"ba394ef6-bd88-44e8-bf64-cf9a9fc9a14b","order_by":2,"name":"Saeed Salehi","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA00lEQVRIiWNgGAWjYLCCD39AZPoDhgcMB3gYmInQwTizDUTlGDAkEKuFmbcBrIUBpIWwcvP25mOfbRvs5PjZcxg/JFTckWFg532AV4vMmWPJs3P+JBtL9jx/LJFw5hnQYewGeLVISOQYM+ewMSduuJFgIJHYdhiohQ2/w8BaLNjq6/ffSDD+kfiPWC0MbIeBViSYSSQ2EKOF51gyY2/bccMZZ96YWSQcO8zDRlALe/Nhhh9/quX529Mf3/hQc9ien/8Yfi2YgIAdo2AUjIJRMAqIAQCEYT+Dql8+KQAAAABJRU5ErkJggg==","orcid":"","institution":"University of Tabriz","correspondingAuthor":true,"prefix":"","firstName":"Saeed","middleName":"","lastName":"Salehi","suffix":""}],"badges":[],"createdAt":"2024-03-05 07:47:21","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4015804/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4015804/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":53846162,"identity":"4ffb4387-85fd-4e92-86ba-8309ba35593a","added_by":"auto","created_at":"2024-04-01 08:38:42","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":247001,"visible":true,"origin":"","legend":"","description":"","filename":"ActaInf.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4015804/v1_covered_493359b8-46d5-4464-aa37-f5ebf6a3bc36.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"How (not) to Compute the Halting Probability.","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"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":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Chaitin’s Constant, The Omega Number, Halting Probability, Probability Measure, Kolmogorov Axioms, Algorithmic Information Theory.","lastPublishedDoi":"10.21203/rs.3.rs-4015804/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4015804/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eWe study Chaitin’s well-known constant number Omega, and show that it is not a probability of halting the randomly chosen input-free programs. 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