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Bir Boyutlu Hücresel Dönüşümlerin Terslenebilirliği

Year 2022, , 505 - 513, 30.06.2022
https://doi.org/10.35193/bseufbd.1082679

Abstract

Bu makalede bir boyutlu sonlu lineer hücresel dönüşümler üzerinde çalışıyoruz. Sıfır Sınır Şartı altında yerel kurallar yardımıyla temsili matrisi elde ettik. Elde edilen bu matrislerin sonlu cisimler üzerinde hangi şartlar altında tersinin olup olmadığını veren bir algoritma tanımladık. Bu aynı zamanda bize hücresel dönüşüm ailesinin terslenebilirliği hakkında fikir veriyor. Son olarak hücresel dönüşümlerin bu ailelerine bazı örnekler veriyoruz.

Thanks

Makalenin kalitesini ve okunabilirliğini önemli ölçüde arttıran, hakemlerin değerli ve yapıcı yorumları için teşekkürlerimi sunarım.

References

  • Chang, C.C. & Yang Y. C., (2020). Characterization of reversible intermediate boundary cellular automata. Journal of Statistical Mechanics: Theory and Experiment, 1, 1-13.
  • Cinkir, Z., Akın, H. &, Siap, İ., (2011). Reversibility of 1D cellular automata with periodic boundary over finite fields Z_{p}”. Journal of Statistical Physics, 143 (4), 807-823.
  • Das, A.K. & Chaudhurı, P. P. (1993).Vector space theoretic analysis of additive cellular automata and its applications for pseudo exhaustive test pattern generation. IEEE Trans. on Computers 42 (3), 340–35.
  • Del Rey, A. M. & Rodriguez S., G. (2011). Reversibility of linear cellular automata, Applied Mathematics and Computation,217 (21), 8360-8366.
  • Hedlund, G.A. (1969). Endomorphisms and automorp hism of full shift dynamical system. Mathematical System Theory, 3, 320–375.
  • Köroğlu, M.E. (2012). Hücresel Dönüşümlerle Hata Düzelten Kodlar. Doktora Tezi, Yıldız Teknik Üniversitesi Fen Bilimleri Enstitüsü, İstanbul, 107.
  • Neumann, V. (1966). The theory of self-reproducing automata, Univ. of ıllinois Press, Urbana.
  • Siap, İ, Akın, H. & Koroglu, M.E. (2013). The reversibility of (2r +1)-cyclic rule cellular automata. TWMS J. App. & Eng. Math, 2, 215-225.
  • Wolfram, S., (1983). Statistical mechanics of cellular automata, Rev. Mod. Phys. 55 (3), 601–644.
  • Khan, A.R. Choudhury, P.P. Dihidar, K. Mitra, S. & Sarkar, P. (1997). VLSI architecture of a cellular automata machine, Computers and Mathematics with Applications, 33, (5) 79–94.
  • Siap, İ, Akın, H. & F. Sah, (2011). Characterization of two dimensional cellular automata over ternary fields, Journal Of The Franklin Institute. 348 (2011), 1258–1275.
  • Başar, F, (2002). Lineer Cebir. Uğurel Matbaası, Malatya, 468.
  • Akın, H. (2021). Description of Reversibility of 9-Cyclic 1D Finite Linear Cellular Automata with Periodic Boundary Conditions, Journal of Cellular Automata, 16, 127–151.

Reversibility of One-Dimensional Cellular Automata

Year 2022, , 505 - 513, 30.06.2022
https://doi.org/10.35193/bseufbd.1082679

Abstract

In this paper, we study one dimensional finite linear cellular automata. We obtained the representative matrix with the help of local rules under the null boundary condition. We have defined an algorithm that gives whether these obtained matrices have an inverse on finite fields under what conditions. This also gives us an idea of the reversibility of the cellular automata family. Finally, we give some examples of these families of cellular automata.

References

  • Chang, C.C. & Yang Y. C., (2020). Characterization of reversible intermediate boundary cellular automata. Journal of Statistical Mechanics: Theory and Experiment, 1, 1-13.
  • Cinkir, Z., Akın, H. &, Siap, İ., (2011). Reversibility of 1D cellular automata with periodic boundary over finite fields Z_{p}”. Journal of Statistical Physics, 143 (4), 807-823.
  • Das, A.K. & Chaudhurı, P. P. (1993).Vector space theoretic analysis of additive cellular automata and its applications for pseudo exhaustive test pattern generation. IEEE Trans. on Computers 42 (3), 340–35.
  • Del Rey, A. M. & Rodriguez S., G. (2011). Reversibility of linear cellular automata, Applied Mathematics and Computation,217 (21), 8360-8366.
  • Hedlund, G.A. (1969). Endomorphisms and automorp hism of full shift dynamical system. Mathematical System Theory, 3, 320–375.
  • Köroğlu, M.E. (2012). Hücresel Dönüşümlerle Hata Düzelten Kodlar. Doktora Tezi, Yıldız Teknik Üniversitesi Fen Bilimleri Enstitüsü, İstanbul, 107.
  • Neumann, V. (1966). The theory of self-reproducing automata, Univ. of ıllinois Press, Urbana.
  • Siap, İ, Akın, H. & Koroglu, M.E. (2013). The reversibility of (2r +1)-cyclic rule cellular automata. TWMS J. App. & Eng. Math, 2, 215-225.
  • Wolfram, S., (1983). Statistical mechanics of cellular automata, Rev. Mod. Phys. 55 (3), 601–644.
  • Khan, A.R. Choudhury, P.P. Dihidar, K. Mitra, S. & Sarkar, P. (1997). VLSI architecture of a cellular automata machine, Computers and Mathematics with Applications, 33, (5) 79–94.
  • Siap, İ, Akın, H. & F. Sah, (2011). Characterization of two dimensional cellular automata over ternary fields, Journal Of The Franklin Institute. 348 (2011), 1258–1275.
  • Başar, F, (2002). Lineer Cebir. Uğurel Matbaası, Malatya, 468.
  • Akın, H. (2021). Description of Reversibility of 9-Cyclic 1D Finite Linear Cellular Automata with Periodic Boundary Conditions, Journal of Cellular Automata, 16, 127–151.
There are 13 citations in total.

Details

Primary Language Turkish
Journal Section Articles
Authors

Ferhat Şah 0000-0003-4847-9180

Publication Date June 30, 2022
Submission Date March 4, 2022
Acceptance Date April 26, 2022
Published in Issue Year 2022

Cite

APA Şah, F. (2022). Bir Boyutlu Hücresel Dönüşümlerin Terslenebilirliği. Bilecik Şeyh Edebali Üniversitesi Fen Bilimleri Dergisi, 9(1), 505-513. https://doi.org/10.35193/bseufbd.1082679