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Boolean algebras as a tool to implement and analyze hypercompositional structures

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  • Talotti, Enrico
  • Cristea, Irina

Abstract

The manuscript presents a novel approach for implementing and analyzing algebraic hypercompositional structures by integrating concepts from computer science. Specifically, a library written in Rust, designed to generate and explore such structures, is built. The framework supports the identification of various hypercompositional structures, including (semi)hypergroups, transposition hypergroups, quasicanonical and canonical hypergroups, along with their associated substructures. Additionally, some tools for detecting particular elements such as scalar elements, identity elements, and scalar identities, are provided. By leveraging Boolean algebra, each hypercompositional structure is encoded as a binary string that contains all relevant structural information, enabling efficient computation and analysis.

Suggested Citation

  • Talotti, Enrico & Cristea, Irina, 2026. "Boolean algebras as a tool to implement and analyze hypercompositional structures," Applied Mathematics and Computation, Elsevier, vol. 516(C).
    • Handle: RePEc:eee:apmaco:v:516:y:2026:i:c:s009630032500565x
    DOI: 10.1016/j.amc.2025.129840
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    References listed on IDEAS

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    1. Gerasimos Massouros & Christos Massouros, 2020. "Hypercompositional Algebra, Computer Science and Geometry," Mathematics, MDPI, vol. 8(8), pages 1-33, August.
    2. Christos G. Massouros & Gerasimos G. Massouros, 2023. "On the Borderline of Fields and Hyperfields," Mathematics, MDPI, vol. 11(6), pages 1-35, March.
    3. Andromeda Pătraşcu Sonea & Ciprian Chiruţă, 2024. "Optimizing HX-Group Compositions Using C ++: A Computational Approach to Dihedral Group Hyperstructures," Mathematics, MDPI, vol. 12(22), pages 1-14, November.
    4. Milica Kankaras & Irina Cristea, 2020. "Fuzzy Reduced Hypergroups," Mathematics, MDPI, vol. 8(2), pages 1-12, February.
    5. Christos G. Massouros & Naveed Yaqoob, 2021. "On the Theory of Left/Right Almost Groups and Hypergroups with their Relevant Enumerations," Mathematics, MDPI, vol. 9(15), pages 1-31, August.
    6. Christos Massouros & Gerasimos Massouros, 2021. "An Overview of the Foundations of the Hypergroup Theory," Mathematics, MDPI, vol. 9(9), pages 1-41, April.
    Full references (including those not matched with items on IDEAS)

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