Semigroup Actions for Crop Growth and Pest Control: Minimal Intervention Bases via Pruning Algorithms

Semigroup Actions for Crop Growth and Pest Control: Minimal Intervention Bases via Pruning Algorithms | 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 Semigroup Actions for Crop Growth and Pest Control: Minimal Intervention Bases via Pruning Algorithms Akak, Eyo Offiong, Marshal I. Sampson, Ubong D. Akpan, Ekere S. Udofia This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9567992/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 This paper extends semigroup-basis pruning algorithms [15] to a control framework for crop growth and pest-management interventions. Interventions are modeled as semigroup actions on a finite state space representing crop and pest conditions, where pruning eliminates redundant transformations while preserving reachability. Using dependence sets D(S) and decomposition maps gS, we derive minimal generating intervention bases that achieve equivalent control objectives with reduced structural and computational complexity. Formal algebraic methods are being increasingly recognized as viable tools for reasoning about computational processes in agriculture, and the subtle relationship between minimal generating sets and maximal independent subsets motivates algorithmic approaches to basis computation [23]. Theoretical results establish correctness and termination of the pruning algorithms, and a worked example demonstrates their application to a finite transformation semigroup describing crop-state transitions. The framework is further extended to a cost-sensitive pruning setting that incorporates resource costs and operational constraints into the optimization process, enabling efficient and sustainable intervention planning. A complementary simulation platform implements the algorithms computationally, allowing performance evaluation through metrics such as efficiency ratio, reachability rate, and pruning gain. Overall, the study demonstrates that semigroup-based pruning offers a mathematically rigorous and computationally viable foundation for data-driven agricultural control and decision support. Algebra Applied Mathematics Computational Mathematics Semigroup actions Basis pruning algorithms Minimal generating sets Cost-sensitive intervention planning Transformation semigroups Full Text Additional Declarations The authors declare no competing interests. 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. 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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-9567992","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":631905025,"identity":"0918395a-a679-4e9a-8b9b-4a7fa51cf61a","order_by":0,"name":"Akak, Eyo Offiong","email":"","orcid":"","institution":"Department of Mathematics, Akwa Ibom State University, Ikot Akpaden, Nigeria","correspondingAuthor":false,"prefix":"","firstName":"Eyo","middleName":"Offiong","lastName":"Akak","suffix":""},{"id":631905026,"identity":"8bd6fc72-3024-458b-8fb5-a546a179d359","order_by":1,"name":"Marshal I. 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Interventions are modeled as semigroup actions on a finite state space representing crop and pest conditions, where pruning eliminates redundant transformations while preserving reachability. Using dependence sets D(S) and decomposition maps gS, we derive minimal generating intervention bases that achieve equivalent control objectives with re\u0002duced structural and computational complexity. Formal algebraic methods are being increasingly recognized as viable tools for reasoning about computational processes in agriculture, and the subtle relationship between minimal generating sets and maximal independent subsets motivates algorithmic approaches to basis computation [23]. Theoretical results establish correctness and termination of the pruning algorithms, and a worked example demonstrates their application to a finite trans\u0002formation semigroup describing crop-state transitions. The framework is further extended to a cost-sensitive pruning setting that incorporates resource costs and operational constraints into the optimization process, enabling efficient and sus\u0002tainable intervention planning. A complementary simulation platform implements the algorithms computationally, allowing performance evaluation through metrics such as efficiency ratio, reachability rate, and pruning gain. 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