Self-similarity of linear cellular automata
نویسندگان
چکیده
منابع مشابه
Quasi-Linear Cellular Automata
Simulating a cellular automaton (CA) for t time-steps into the future requires t serial computation steps or t parallel ones. However, certain CAs based on an Abelian group, such as addition mod 2, are termed linear because they obey a principle of superposition. This allows them to be predicted efficiently, in serial time O(t) or O(log t) in parallel. In this paper, we generalize this by looki...
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Abstract In this paper, we present a possible implementation of arithmetic functions (notably, addition and multiplication) using self-replicating cellular automata. The operations are performed by storing a dedicated program (sequence of states) on self-replicating loops, and letting the loops retrieve the operands, exchange data among themselves, and perform the calculations according to a se...
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Linear cellular automata have a canonical representation in terms of labeled de Bruijn graphs. We will show that these graphs, construed as semiautomata, provide a natural setting for the study of cellular automata. For example, we give a simple algorithm to determine reversibility and surjectivity of the global maps. We also comment on Wolfram’s question about the growth rates of the minimal f...
متن کاملLinear Cellular Automata and de Bruijn Automata
Linear cellular automata have a canonical representation in terms of labeled de Bruijn graphs. We will show that these graphs, construed as semiau-tomata, provide a natural setting for the study of cellular automata. For example, we give a simple algorithm to determine reversibility and surjectivity of the global maps. We also comment on Wolfram's question about the growth rates of the minimal ...
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ژورنال
عنوان ژورنال: Journal of Computer and System Sciences
سال: 1992
ISSN: 0022-0000
DOI: 10.1016/0022-0000(92)90007-6