Brains, machines, and mathematics (2nd ed.)
Brains, machines, and mathematics (2nd ed.)
Learning Patterns and Pattern Sequences by Self-Organizing Nets of Threshold Elements
IEEE Transactions on Computers
Fault tolerant cellular spaces
Journal of Computer and System Sciences
Fault-Tolerant Structures: Towards Robust Self-Replication in a Probabilistic Environment
ECAL '01 Proceedings of the 6th European Conference on Advances in Artificial Life
Massively Parallel Pattern Recognition with Link Failures
SOFSEM '00 Proceedings of the 27th Conference on Current Trends in Theory and Practice of Informatics
Nature-based problems in cellular automata
CiE'11 Proceedings of the 7th conference on Models of computation in context: computability in Europe
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Cellular automata have some useful characteristics because of the uniformity of the cellular structure. Here we use geometrical codings to design fault tolerant cellular automata which simulate given cellular automata. First, the concept of a group graph is introduced as a mathematical description of the cellular structure. Geometrical codings are then defined using its algebraic properties. Under the condition of K-separated misoperation, i.e., at each state transition at most one cell in any K-neighborhood of the cellular space can possibly misoperate, it is possible to design cellular automata which have detection capabity or correction capability. Some examples are also presented using the two-dimensional lattice and the hexagonal cellular space.