A characterization of important algorithms for quantum-dot cellular automata
Information Sciences: an International Journal
Regular biosequence pattern matching with cellular automata
Information Sciences—Applications: An International Journal
Matrix algebraic formulae concerning some exceptional rules of two-dimensional cellular automata
Information Sciences: an International Journal
Theory of Self-Reproducing Automata
Theory of Self-Reproducing Automata
On cellular automata over Galois rings
Information Processing Letters
Computing with random quantum dot repulsion
Information Sciences: an International Journal
Some clarifications of the concept of a Garden-of-Eden configuration
Journal of Computer and System Sciences
Garden of eden configurations for 2-D cellular automata with rule 2460N
Information Sciences: an International Journal
Structure and reversibility of 2D hexagonal cellular automata
Computers & Mathematics with Applications
Fluctuation-driven computing on number-conserving cellular automata
Information Sciences: an International Journal
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Several studies [A.R. Khan, P.P. Choudhury, K. Dihidar, S. Mitra, P. Sarkar, VLSI architecture of a cellular automata, Comput. Math. Appl. 33 (1997) 79-94; A.R. Khan, P.P. Choudhury, K. Dihidar, R. Verma, Text compression using two-dimensional cellular automata, Comput. Math. Appl. 37 (1999) 115-127; K. Dihidar, P.P. Choudhury, Matrix algebraic formulae concerning some exceptional rules of two-dimensional cellular automata, Inf. Sci. 165 (2004) 91-101] have explored a new rule convention for two-dimensional (2-D) nearest neighborhood linear cellular automata (CA) with null and periodic boundary conditions. A variety of applications of the rule convention have been illustrated, and the VLSI architecture of cellular automata machine (CAM) has been proposed. However, most of the studies address the issue of the kernel dimension of 2-D CA, and many other important characteristics of CA, such as Garden of Eden (GOE), maximal transient length, maximal cycle length, etc., have not been explored. In this paper, by exploiting matrix algebra in GF(2) (the Galois field with two elements), we attempt to characterize the behavior of a specific rule, which is not covered in existing work but accords with the same convention. A necessary and sufficient condition is given to ensure that a given configuration is a GOE. Meanwhile, we propose some algorithms to determine the number of GOEs, the maximal transient length, and the maximal cycle length in a 2-D CA.