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- W2913459483 abstract "We study the dynamical behavior of linear higher-order cellular automata (HOCA) over (mathbb {Z}_m). In standard cellular automata the global state of the system at time t only depends on the state at time (t-1), while in HOCA it is a function of the states at time (t-1), ..., (t-n), where (nge 1) is the memory size. In particular, we provide easy-to-check necessary and sufficient conditions for a linear HOCA over (mathbb {Z}_m) of memory size n to be sensitive to the initial conditions or equicontinuous. Our characterizations of sensitivity and equicontinuity extend the ones shown in [23] for linear cellular automata (LCA) over (mathbb {Z}_m^n) in the case (n=1). We also prove that linear HOCA over (mathbb {Z}_m) of memory size n are indistinguishable from a subclass of LCA over (mathbb {Z}_m^n). This enables to decide injectivity and surjectivity for linear HOCA over (mathbb {Z}_m) of memory size n by means of the decidable characterizations of injectivity and surjectivity provided in [2] and [20] for LCA over (mathbb {Z}^n_m)." @default.
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- W2913459483 date "2019-01-01" @default.
- W2913459483 modified "2023-09-25" @default.
- W2913459483 title "Decidability of Sensitivity and Equicontinuity for Linear Higher-Order Cellular Automata" @default.
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- W2913459483 doi "https://doi.org/10.1007/978-3-030-13435-8_7" @default.
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