Reversibility Algorithm for 2D Cellular Automata with Reflective Condition

S. Redjepova, E. Acarb, S. Uguzc aFaculty of Computer Engineering, Tashkent University of Information Technologies, Tashkent, 100202, Uzbekistan bDepartment of Mathematics, Harran University, Sanliurfa, 63120, Turkey cSU Mathematics and Science Academy, S. Urfa, 63100, Turkey

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In the present paper, there are studied main theoretical views of two-dimensional (2D) linear uniform cellular automata with reflective boundary condition over the ternary field, i.e. three states spin case or Z3. We set up a relation between reversibility of cellular automata and characterization of 2D uniform linear cellular automata with this special boundary conditions by using of the matrix theory. In near future, these cellular automata can be found in many different real life applications, e.g. computability theory, theoretical biology, image processing area, textile design, video processing, etc.

DOI:10.12693/APhysPolA.134.454 topics: reversibility, 2D CA, rule matrix, reflective boundary, ternary field