Abstract
This paper surveys some old results about linear shift registers and restates them in the context of additive automata networks. The addition of new results allows an almost complete description of the dynamical behavior of additive automata networks. The computational complexity aspects of deciding such behaviors are also discussed.
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Notes
- 1.
Recall that h injective means \(h(\mathcal {U})=h(\mathcal {V}) \Rightarrow \mathcal {U}=\mathcal {V}\). But since h is a homomorphism it comes \(h(\mathcal {U})-h(\mathcal {V})=0 \iff h(\mathcal {U}-\mathcal {V})=0 \iff (\mathcal {U}-\mathcal {V})\in \ker (h)\), hence \(\ker (h)=\{0\} \iff h \text { injective}\).
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Formenti, E., Papazian, C., Richard, A., Scribot, PA. (2022). From Additive Flowers to Additive Automata Networks. In: Adamatzky, A. (eds) Automata and Complexity. Emergence, Complexity and Computation, vol 42. Springer, Cham. https://doi.org/10.1007/978-3-030-92551-2_18
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