Abstract
Cellular automata (CAs) consist of an bi-infinite array of identical cells, each of which may take one of a finite number of possible states. The entire array evolves in discrete time steps by iterating a global evolution G. Further, this global evolution G is required to be shift-invariant (it acts the same everywhere) and causal (information cannot be transmitted faster than some fixed number of cells per time step). At least in the classical [7], reversible [11] and quantum cases [1], these two top-down axiomatic conditions are sufficient to entail more bottom-up, operational descriptions of G. We investigate whether the same is true in the probabilistic case.
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Arrighi, P., Fargetton, R., Nesme, V., Thierry, E. (2011). Applying Causality Principles to the Axiomatization of Probabilistic Cellular Automata. In: Löwe, B., Normann, D., Soskov, I., Soskova, A. (eds) Models of Computation in Context. CiE 2011. Lecture Notes in Computer Science, vol 6735. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21875-0_1
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DOI: https://doi.org/10.1007/978-3-642-21875-0_1
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