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Shrinking One-Way Cellular Automata

Abstract : We investigate cellular automata as acceptors for formal languages. In particular, we consider real-time one-way cellular automata ($\text{OCA}$) with the additional property that during a computation any cell of the $\text{OCA}$ has the ability to dissolve itself and we call this model shrinking one-way cellular automata ($\text{SOCA}$). It turns out that real-time $\text{SOCA}$ are more powerful than real-time $\text{OCA}$, since they can accept certain linear-time $\text{OCA}$ languages. Additionally, a construction is provided that enables real-time $\text{SOCA}$ to accept the reversal of real-time iterative array languages. Finally, restricted real-time $\text{SOCA}$ are investigated which are allowed to dissolve only a number of cells that is bounded by some function. In this case, an infinite strict hierarchy of language classes is obtained.
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https://hal.inria.fr/hal-01442469
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Martin Kutrib, Andreas Malcher, Matthias Wendlandt. Shrinking One-Way Cellular Automata. 21st Workshop on Cellular Automata and Discrete Complex Systems (AUTOMATA), Jun 2015, Turku, Finland. pp.141-154, ⟨10.1007/978-3-662-47221-7_11⟩. ⟨hal-01442469⟩

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