IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v12y2024i13p2110-d1429415.html
   My bibliography  Save this article

Simulations and Bisimulations between Weighted Finite Automata Based on Time-Varying Models over Real Numbers

Author

Listed:
  • Predrag S. Stanimirović

    (Faculty of Sciences and Mathematics, University of Niš, Višegradska 33, 18000 Niš, Serbia
    Laboratory “Hybrid Methods of Modelling and Optimization in Complex Systems”, Siberian Federal University, Prosp. Svobodny 79, Krasnoyarsk 660041, Russia)

  • Miroslav Ćirić

    (Faculty of Sciences and Mathematics, University of Niš, Višegradska 33, 18000 Niš, Serbia)

  • Spyridon D. Mourtas

    (Laboratory “Hybrid Methods of Modelling and Optimization in Complex Systems”, Siberian Federal University, Prosp. Svobodny 79, Krasnoyarsk 660041, Russia
    Department of Economics, Division of Mathematics-Informatics and Statistics-Econometrics, National and Kapodistrian University of Athens, Sofokleous 1 Street, 10559 Athens, Greece)

  • Pavle Brzaković

    (Faculty of Applied Management, Economics and Finance, University Business Academy in Novi Sad, Jevrejska 24, 11000 Belgrade, Serbia)

  • Darjan Karabašević

    (Faculty of Applied Management, Economics and Finance, University Business Academy in Novi Sad, Jevrejska 24, 11000 Belgrade, Serbia
    College of Global Business, Korea University, Sejong 30019, Republic of Korea)

Abstract

The zeroing neural network (ZNN) is an important kind of continuous-time recurrent neural network (RNN). Meanwhile, the existence of forward and backward simulations and bisimulations for weighted finite automata (WFA) over the field of real numbers has been widely investigated. Two types of quantitative simulations and two types of bisimulations between WFA are determined as solutions to particular systems of matrix and vector inequations over the field of real numbers R . The approach used in this research is unique and based on the application of a ZNN dynamical evolution in solving underlying matrix and vector inequations. This research is aimed at the development and analysis of four novel ZNN dynamical systems for addressing the systems of matrix and/or vector inequalities involved in simulations and bisimulations between WFA. The problem considered in this paper requires solving a system of two vector inequations and a couple of matrix inequations. Using positive slack matrices, required matrix and vector inequations are transformed into corresponding equations and then the derived system of matrix and vector equations is transformed into a system of linear equations utilizing vectorization and the Kronecker product. The solution to the ZNN dynamics is defined using the pseudoinverse solution of the generated linear system. A detailed convergence analysis of the proposed ZNN dynamics is presented. Numerical examples are performed under different initial state matrices. A comparison between the ZNN and linear programming (LP) approach is presented.

Suggested Citation

  • Predrag S. Stanimirović & Miroslav Ćirić & Spyridon D. Mourtas & Pavle Brzaković & Darjan Karabašević, 2024. "Simulations and Bisimulations between Weighted Finite Automata Based on Time-Varying Models over Real Numbers," Mathematics, MDPI, vol. 12(13), pages 1-26, July.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:13:p:2110-:d:1429415
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/12/13/2110/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/12/13/2110/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Xingyuan Li & Chia-Liang Lin & Theodore E. Simos & Spyridon D. Mourtas & Vasilios N. Katsikis, 2022. "Computation of Time-Varying {2,3}- and {2,4}-Inverses through Zeroing Neural Networks," Mathematics, MDPI, vol. 10(24), pages 1-13, December.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.

      Corrections

      All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:12:y:2024:i:13:p:2110-:d:1429415. See general information about how to correct material in RePEc.

      If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

      If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

      If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

      For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

      Please note that corrections may take a couple of weeks to filter through the various RePEc services.

      IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.