A Graph-Based Inference Framework for Word Deduction under Partial Feedback

A Graph-Based Inference Framework for Word Deduction under Partial Feedback | 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 Article A Graph-Based Inference Framework for Word Deduction under Partial Feedback Dakshi Arora, Prakhar Kumar Srivastava, Ranjib Banerjee This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9222809/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 5 You are reading this latest preprint version Abstract Reasoning under incomplete feedback remains a recurring challenge in intelligentinference systems. We present a computational perspective to examine Jotto, theword deduction problem. The study proposes a graph-based framework for identifying secret words through iterative feedback. In the proposed model, candidatewords are represented as nodes in a lexical overlap network where the sharedletter relationships is captured by the weighted edges. The response received asthe feedback is used as the constraint to prune the nodes that are not consistentwith the received response.Wepropose aformulation that extends conventional treatments of the problem bysupporting variable word lengths of 3-8 letters and accommodates repeated-letterconfigurations as well. This allows the framework to handle a broader range ofdeduction scenarios than traditional fixed-length or isogram-based models. Theconvergence of the solver is verified with an experimental evaluation using 3000automated simulations of different word lengths and repeated letter configuration, showing consistent convergence to the correct solution. Regression analysissuggests a logarithmic trend between word length and the averages number ofiterations required for identification, indicating that longer words tend to providestronger discriminatory information during the deduction process.A computational complexity analysis and an illustrative case study are alsopresented to clarify the behavior of the algorithm. The results suggest thatgraph-based constraint propagation provides a transparent and computationallymanageable approach to reasoning under partial information. Physical sciences/Engineering Physical sciences/Mathematics and computing Graph-based inference Constraint propagation Combinatorial search Intelligent reasoning Entropy reduction Network pruning Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Reviewers invited by journal 29 Apr, 2026 Editor invited by journal 31 Mar, 2026 Editor assigned by journal 26 Mar, 2026 Submission checks completed at journal 26 Mar, 2026 First submitted to journal 25 Mar, 2026 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-9222809","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":634292425,"identity":"e2a57b2a-a4d2-4427-9cfb-cef5471d8b1a","order_by":0,"name":"Dakshi Arora","email":"","orcid":"","institution":"BML Munjal University","correspondingAuthor":false,"prefix":"","firstName":"Dakshi","middleName":"","lastName":"Arora","suffix":""},{"id":634292426,"identity":"9bafb436-aed4-4f2d-8ad1-b3b92c6b5abd","order_by":1,"name":"Prakhar Kumar Srivastava","email":"","orcid":"","institution":"BML Munjal University","correspondingAuthor":false,"prefix":"","firstName":"Prakhar","middleName":"Kumar","lastName":"Srivastava","suffix":""},{"id":634292427,"identity":"ad1583c9-bfde-4b17-8d16-dc1f99d43eb0","order_by":2,"name":"Ranjib Banerjee","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABFklEQVRIiWNgGAWjYJACg8QGhgQwS4KBQQ4uzEasFmOitDAwwrQAAVA7AWDefvZAwcMdDHn8s5uPfbCosEnfcLv58AeGGjsGPmnsumXO5CUYJJ5hKJa4cyx5hsSZtNwNd46lSTAcS2ZgkzmAVYsEQ46BQWIb0D03cowZJNsO5264kWMG9MgBBjaJBOxa+N9AtMy/kf+ZQfLf/3QDIOMDwz88WiSgtgANZ2aQbDiQYHAjh0GCsQ2fFpAtZySKDW+kGTNIHEs2nHnnmJlEYl8yD26H5ZgZ/txhkyd3I/kxs0SNnTzf7ebHHz58s5OTn4FdCxCwGYDjEAiYJSAhwgCKJh5c6kEKH8BYjB9gWkbBKBgFo2AUIAEAqURbCnoVyt0AAAAASUVORK5CYII=","orcid":"","institution":"University of Petroleum and Energy Studies","correspondingAuthor":true,"prefix":"","firstName":"Ranjib","middleName":"","lastName":"Banerjee","suffix":""}],"badges":[],"createdAt":"2026-03-25 12:08:23","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-9222809/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9222809/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":108696488,"identity":"969e52a8-8769-4344-b1b5-34b96f047d88","added_by":"auto","created_at":"2026-05-07 11:57:06","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1810277,"visible":true,"origin":"","legend":"","description":"","filename":"ScientificReportsJotto.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9222809/v1_covered_598a95e1-2faa-425c-b2f4-20163299c274.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"A Graph-Based Inference Framework for Word Deduction under Partial Feedback","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":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"Graph-based inference, Constraint propagation, Combinatorial search, Intelligent reasoning, Entropy reduction, Network pruning","lastPublishedDoi":"10.21203/rs.3.rs-9222809/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9222809/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"Reasoning under incomplete feedback remains a recurring challenge in intelligentinference systems. We present a computational perspective to examine Jotto, theword deduction problem. The study proposes a graph-based framework for identifying secret words through iterative feedback. In the proposed model, candidatewords are represented as nodes in a lexical overlap network where the sharedletter relationships is captured by the weighted edges. The response received asthe feedback is used as the constraint to prune the nodes that are not consistentwith the received response.Wepropose aformulation that extends conventional treatments of the problem bysupporting variable word lengths of 3-8 letters and accommodates repeated-letterconfigurations as well. This allows the framework to handle a broader range ofdeduction scenarios than traditional fixed-length or isogram-based models. Theconvergence of the solver is verified with an experimental evaluation using 3000automated simulations of different word lengths and repeated letter configuration, showing consistent convergence to the correct solution. Regression analysissuggests a logarithmic trend between word length and the averages number ofiterations required for identification, indicating that longer words tend to providestronger discriminatory information during the deduction process.A computational complexity analysis and an illustrative case study are alsopresented to clarify the behavior of the algorithm. 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