Tri-Paradigm analysis of computational complexity in NP-Hard Sudoku solvers using explainable AI

Tri-Paradigm analysis of computational complexity in NP-Hard Sudoku solvers using explainable AI | 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 Tri-Paradigm analysis of computational complexity in NP-Hard Sudoku solvers using explainable AI Rajan Thangamani, Pallavi R This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8392292/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 Sudoku is a demanding test of computational complexity and constraint satisfaction problems. This work develops a comprehensive and replicable benchmark that reformulates 9×9 Sudoku puzzles under three solver paradigms of constraint programming (CP), Boolean satisfiability (SAT), and integer programming (IP) in order to assess efficacy and explainability. For each paradigm, a parametrically equivalent model is implemented and solved with common datasets and experiment control conditions. We measure wall-clock running time, peak memory usage, and paradigm-data related measures of effort in backtracks or fails in CP, decisions or conflicts with conflict-driven clause learning(CDCL) in SAT, and branch & bound nodes or linear program relaxations in IP. Aggregate trends provide empirical evidence consistent with NP-hard/NP-complete behavior: runtime grows approximately exponentially with constraint tightness, while memory remains nearly flat for standard grids. An explicit Explainable Artificial Intelligence (XAI) trade-off emerges. SAT delivers the lowest runtime via clause learning and pruning; CP yields the most interpretable reasoning through transparent propagation and traceable search; IP offers algebraic auditability and flexibility for optimization variants but incurs higher search effort on pure feasibility. The benchmark, figures, and tables establish a verifiable claim–evidence link and supply a practical baseline for integrating explainability metrics into analytic decision pipelines. The results inform the design of intelligent and explainable solver architectures, aligning with the aim of Intelligent systems with applications. We conclude with a roadmap toward hybrid CP–SAT approaches that retain CP-level interpretability while leveraging SAT-level efficiency. Sudoku NP-complete Constraint programming SAT Integer programming Explainable AI 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-8392292","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":562282587,"identity":"1be2f8aa-f9a6-40a7-bc69-fea79ee40032","order_by":0,"name":"Rajan 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This work develops a comprehensive and replicable benchmark that reformulates 9\u0026times;9 Sudoku puzzles under three solver paradigms of constraint programming (CP), Boolean satisfiability (SAT), and integer programming (IP) in order to assess efficacy and explainability. For each paradigm, a parametrically equivalent model is implemented and solved with common datasets and experiment control conditions. We measure wall-clock running time, peak memory usage, and paradigm-data related measures of effort in backtracks or fails in CP, decisions or conflicts with conflict-driven clause learning(CDCL) in SAT, and branch \u0026amp; bound nodes or linear program relaxations in IP. Aggregate trends provide empirical evidence consistent with NP-hard/NP-complete behavior: runtime grows approximately exponentially with constraint tightness, while memory remains nearly flat for standard grids. An explicit Explainable Artificial Intelligence (XAI) trade-off emerges. SAT delivers the lowest runtime via clause learning and pruning; CP yields the most interpretable reasoning through transparent propagation and traceable search; IP offers algebraic auditability and flexibility for optimization variants but incurs higher search effort on pure feasibility. The benchmark, figures, and tables establish a verifiable claim\u0026ndash;evidence link and supply a practical baseline for integrating explainability metrics into analytic decision pipelines. The results inform the design of intelligent and explainable solver architectures, aligning with the aim of Intelligent systems with applications. 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