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Numerical P Systems with Thresholds and Petri Nets

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Bio-Inspired Computing: Theories and Applications (BIC-TA 2023)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 2061))

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Abstract

Membrane computing provides efficient computing devices for broad applications due to its distributed storage and the parallel processing. As computing devices in membrane computing, numerical P systems with thresholds (NPT systems) are proven to be Turing universal, and their computational and operational semantics need to be further investigated. In this work, the intrinsic relationship between NPT systems and Petri nets is concerned. The ingredients of Petri nets are associated with the elements of numerical variables in NPT systems, and the operations of Petri nets are associated with the evolutions of NPT systems. The results on the boundedness and reachability of NPT systems are obtained by using the relationship between NPT systems and Petri nets.

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References

  1. Assaf, G., Heiner, M., Liu, F.: Coloured fuzzy petri nets for modelling and analysing membrane systems. Biosystems 212, 104592 (2022)

    Article  Google Scholar 

  2. Buiu, C., Florea, A.G.: Membrane computing models and robot controller design, current results and challenges. J. Membr. Comput. 1(4), 262–269 (2019)

    Article  MathSciNet  Google Scholar 

  3. Díaz-Pernil, D., Gutiérrez-Naranjo, M.A., Peng, H.: Membrane computing and image processing: a short survey. J. Membr. Comput. 1, 58–73 (2019)

    Article  MathSciNet  Google Scholar 

  4. Duan, Y., Rong, H., Qi, D., Valencia-Cabrera, L., Zhang, G., Pérez-Jiménez, M.J.: A review of membrane computing models for complex ecosystems and a case study on a complex giant panda system. Complexity 2020, 1–26 (2020)

    Google Scholar 

  5. Kosaraju, S.R.: Decidability of reachability in vector addition systems. In: 14th Annual ACM Symposium on Theory of Computing, San Francisco, pp. 267–281 (1982)

    Google Scholar 

  6. Lambert, J.L.: A structure to decide reachability in petri nets. Theoret. Comput. Sci. 99, 79–104 (1992)

    Article  MathSciNet  Google Scholar 

  7. Lipton, R.J.: The reachability problem requires exponential space. Department of Computer Science, Yale University (1976)

    Google Scholar 

  8. Liu, F., Heiner, M.: Petri nets for modeling and analyzing biochemical reaction networks. In: Chen, M., Hofestädt, R. (eds.) Approaches in Integrative Bioinformatics, pp. 245–272. Springer, Heidelberg (2014). https://doi.org/10.1007/978-3-642-41281-3_9

    Chapter  Google Scholar 

  9. Liu, L., Yi, W., Yang, Q., Peng, H., Wang, J.: Small universal numerical P systems with thresholds for computing functions. Fund. Inform. 176(1), 43–59 (2020)

    MathSciNet  Google Scholar 

  10. Pan, L., Zhang, Z., Wu, T., Xu, J.: Numerical P systems with production thresholds. Theoret. Comput. Sci. 673, 30–41 (2017)

    Article  MathSciNet  Google Scholar 

  11. Păun, Gh.: Computing with membranes. J. Comput. Syst. Sci. 61(1), 108–143 (2000)

    Article  MathSciNet  Google Scholar 

  12. Păun, Gh., Păun, R.: Membrane computing and economics: numerical P systems. Fund. Inform. 73(1), 213–227 (2006)

    MathSciNet  Google Scholar 

  13. Qi, Z., You, J., Mao, H.: P systems and petri nets. In: Martín-Vide, C., Mauri, G., Păun, G., Rozenberg, G., Salomaa, A. (eds.) WMC 2003. LNCS, vol. 2933, pp. 286–303. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-24619-0_21

    Chapter  Google Scholar 

  14. Rackoff, C.: The covering and boundedness problem for vector addition systems. Theoret. Comput. Sci. 6, 223–231 (1978)

    Article  MathSciNet  Google Scholar 

  15. Rong, H., Duan, Y., Zhang, G.: A bibliometric analysis of membrane computing (1998–2019). J. Membr. Comput. 4(2), 177–207 (2022)

    Article  MathSciNet  Google Scholar 

  16. Rozenberg, G., Thiagarajan, P.S.: Petri nets: basic notions, structure, behaviour. Curr. Trends Concurr.: Overviews Tutor. 585–668 (1986)

    Google Scholar 

  17. Song, B., Li, K., Orellana-Martín, D., Pérez-Jiménez, M.J., Pérez-Hurtado, I.: A survey of nature-inspired computing: membrane computing. ACM Comput. Surv. (CSUR) 54(1), 1–31 (2021)

    Article  Google Scholar 

  18. Zhang, Z., Pan, L.: Numerical P systems with thresholds. Int. J. Comput. Commun. Control 11(2), 292–304 (2016)

    Article  Google Scholar 

  19. Zhang, Z., Su, Y., Pan, L.: The computational power of enzymatic numerical P systems working in the sequential mode. Theoret. Comput. Sci. 724, 3–12 (2018)

    Article  MathSciNet  Google Scholar 

  20. Zhang, Z., Wu, T., Pan, L.: On string languages generated by sequential numerical P systems. Fund. Inform. 145(4), 485–509 (2016)

    MathSciNet  Google Scholar 

  21. Zhang, Z., Wu, T., Pan, L., Păun, Gh.: On string languages generated by numerical P systems. Roman. J. Inf. Sci. Technol. 18(3), 273–295 (2015)

    Google Scholar 

  22. Zhang, Z., Wu, T., Păun, A., Pan, L.: Numerical P systems with migrating variables. Theoret. Comput. Sci. 641, 85–108 (2016)

    Article  MathSciNet  Google Scholar 

  23. Zhang, Z., Wu, T., Păun, A., Pan, L.: Universal enzymatic numerical P systems with small number of enzymatic variables. Sci. China Inf. Sci. 61, 1–12 (2018)

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Jiangxi Engineering Technology Research Center of Nuclear Geoscience Data Science and System, Jiangxi Engineering Laboratory on Radioactive Geoscience and Big Data Technology, School of Information Engineering, East China University of Technology, Nanchang, 330013, China

    Luping Zhang & Zhimeng Zhang

Authors
  1. Luping Zhang
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  2. Zhimeng Zhang
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Correspondence to Luping Zhang .

Editor information

Editors and Affiliations

  1. Huazhong University of Science and Technology, Wuhan, China

    Linqiang Pan

  2. Central South University, Changsha, China

    Yong Wang

  3. Huazhong University of Science and Technology, Wuhan, China

    Jianqing Lin

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© 2024 The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.

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Zhang, L., Zhang, Z. (2024). Numerical P Systems with Thresholds and Petri Nets. In: Pan, L., Wang, Y., Lin, J. (eds) Bio-Inspired Computing: Theories and Applications. BIC-TA 2023. Communications in Computer and Information Science, vol 2061. Springer, Singapore. https://doi.org/10.1007/978-981-97-2272-3_25

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  • DOI: https://doi.org/10.1007/978-981-97-2272-3_25

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  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-97-2271-6

  • Online ISBN: 978-981-97-2272-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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