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State Machines and Hypergroups

Author

Listed:
  • Gerasimos G. Massouros

    (School of Social Sciences, Hellenic Open University, Aristotelous 18, GR 26335 Patra, Greece)

  • Christos G. Massouros

    (Core Department, National and Kapodistrian University of Athens, Euripus Campus, GR 34400 Euboia, Greece)

Abstract

State machines are a type of mathematical modeling tool that is commonly used to investigate how a system interacts with its surroundings. The system is thought to be made up of discrete states that change in response to external inputs. The state machines whose environment is a two-element magma are investigated in this study, focusing on the case when the magma is a group or a hypergroup. It is shown that state machines in any two-element magma can only have up to three states. In particular, the quasi-automata and quasi-multiautomata state machines are described and enumerated.

Suggested Citation

  • Gerasimos G. Massouros & Christos G. Massouros, 2022. "State Machines and Hypergroups," Mathematics, MDPI, vol. 10(14), pages 1-25, July.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:14:p:2427-:d:860900
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    References listed on IDEAS

    as
    1. Christos Massouros & Gerasimos Massouros, 2021. "An Overview of the Foundations of the Hypergroup Theory," Mathematics, MDPI, vol. 9(9), pages 1-41, April.
    2. Gerasimos Massouros & Christos Massouros, 2020. "Hypercompositional Algebra, Computer Science and Geometry," Mathematics, MDPI, vol. 8(8), pages 1-33, August.
    3. Irina Cristea & Juš Kocijan & Michal Novák, 2019. "Introduction to Dependence Relations and Their Links to Algebraic Hyperstructures," Mathematics, MDPI, vol. 7(10), pages 1-14, September.
    4. Jan Chvalina & Michal Novák & Bedřich Smetana & David Staněk, 2021. "Sequences of Groups, Hypergroups and Automata of Linear Ordinary Differential Operators," Mathematics, MDPI, vol. 9(4), pages 1-16, February.
    Full references (including those not matched with items on IDEAS)

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