BİR BOYUTLU PERİYODİK SINIR ŞARTLI HÜCRESEL DÖNÜŞÜMLERİN KARAKTERİZASYONU

Öz

Bu çalışmada periyodik sınır şartı altında, bir boyutlu hücresel dönüşümleri inceliyoruz. Zp cismi üzerindeki hesaplamalar için matris cebirlerini kullanıyoruz. Hücresel dönüşümlerin tersini bulmak için bir formül elde ediyoruz. Son olarak, hücresel dönüşümlerin bazı önemli örneklerini veriyoruz.

Anahtar Kelimeler

• Hücresel dönüşümler
• karakteristik matrisler
• sınır şartları
• terslenebilirlik

CHARACTERIZATION OF ONE DIMENSIONAL PERIODIC BOUNDARY CELLULAR AUTOMATA

Öz

In this paper, we investigate one dimensional cellular automata under periodic boundary conditions. We use matrix algebra for calculating over on Zp. We obtain a formula for finding the reversibility of cellular automata. Finally, we give some important examples of cellular automata.

Anahtar Kelimeler

• Boundary condition
• cellular automata
• characteristic matrices
• reversibility

Kaynakça

1. 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.
2. Chang, C.C. & Yang Y. C. (2020). Characterization of reversible intermediate boundary cellular automata. Journal of Statistical Mechanics: Theory and Experiment, 1, 1-13.
3. 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.
4. del Rey, A.M. & Rodriguez, S.G. (2011). Reversibility of linear cellular automata. Applied Mathematics and Computation, 217(21), 8360-8366.
5. Das, A.K. & Chaudhuri, 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.
6. Khan, A.R., Choudhury, P.P., Dihidar, K. & Verma, R. (1999). Text compression using two dimensional cellular automata. Computers and Mathematics with Applications, 37, 115–127.
7. Neumann, J. V. (1966). The theory of self-reproducing automata. Univ. of Illinois Press, Urbana.
8. Wolfram, S., (1983). Statistical mechanics of cellular automata. Rev. Mod. Phys. 55 (3), 601-644.