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Article

Recognizable Languages of k-Forcing Automata

by
Marzieh Shamsizadeh
1,
Mohammad Mehdi Zahedi
2,
Khadijeh Abolpour
3 and
Manuel De la Sen
4,*
1
Department of Mathematics, Behbahan Khatam Alanbia University of Technology, Behbahan 47189-63616, Iran
2
Department of Mathematics, Graduate University of Advanced Technology, Kerman 76311-33131, Iran
3
Department of Mathematics, Islamic Azad University, Shiraz Branch, Shiraz 71987-74731, Iran
4
Institute of Research and Development of Processes, Department of Electricity and Electronics, Faculty of Science and Technology, University of the Basque Country (UPV/EHU), 48940 Leioa, Bizkaia, Spain
*
Author to whom correspondence should be addressed.
Math. Comput. Appl. 2024, 29(3), 32; https://doi.org/10.3390/mca29030032
Submission received: 11 March 2024 / Revised: 21 April 2024 / Accepted: 22 April 2024 / Published: 25 April 2024
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Abstract

In this study, we show that automata theory is also a suitable tool for analyzing a more complex type of the k-forcing process. First, the definition of k-forcing automata is presented according to the definition of k-forcing for graphs. Moreover, we study and discuss the language of k-forcing automata for particular graphs. Also, for some graphs with different k-forcing sets, we study the languages of their k-forcing automata. In addition, for some given recognizable languages, we study the structure of graphs. After that, we show that k-forcing automata arising from isomorph graphs are also isomorph. Also, we present the style of words that can be recognized with k-forcing automata. Moreover, we introduce the structure of graphs the k-forcing automata arising from which recognize some particular languages. To clarify the notions and the results obtained in this study, some examples are submitted as well.
Keywords: graph; zero forcing set; k-forcing; automata; network graph; zero forcing set; k-forcing; automata; network

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MDPI and ACS Style

Shamsizadeh, M.; Zahedi, M.M.; Abolpour, K.; De la Sen, M. Recognizable Languages of k-Forcing Automata. Math. Comput. Appl. 2024, 29, 32. https://doi.org/10.3390/mca29030032

AMA Style

Shamsizadeh M, Zahedi MM, Abolpour K, De la Sen M. Recognizable Languages of k-Forcing Automata. Mathematical and Computational Applications. 2024; 29(3):32. https://doi.org/10.3390/mca29030032

Chicago/Turabian Style

Shamsizadeh, Marzieh, Mohammad Mehdi Zahedi, Khadijeh Abolpour, and Manuel De la Sen. 2024. "Recognizable Languages of k-Forcing Automata" Mathematical and Computational Applications 29, no. 3: 32. https://doi.org/10.3390/mca29030032

APA Style

Shamsizadeh, M., Zahedi, M. M., Abolpour, K., & De la Sen, M. (2024). Recognizable Languages of k-Forcing Automata. Mathematical and Computational Applications, 29(3), 32. https://doi.org/10.3390/mca29030032

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