- Published 2013 in UCNC

Let d ∈ N; then a d-dimensional array A over an alphabet V is a function A : Z → V ∪ {#}, where shape (A) = { v ∈ Z | A (v) 6= # } is finite and # / ∈ V is called the background or blank symbol. The set of all d-dimensional arrays over V is denoted by V ∗d. For v ∈ Z, v = (v1, . . . , vd), the norm of v is ‖v‖ = max {|vi| | 1 ≤ i ≤ d}. The translation τv : Z → Z is defined by τv (w) = w+ v for all w ∈ Z. For any array A ∈ V ∗d, τv (A), the corresponding d-dimensional array translated by v, is defined by (τv (A)) (w) = A (w − v) for all w ∈ Z. For a (non-empty) finite set W ⊂ Z the norm of W is defined as ‖W‖ = max { ‖v − w‖ | v, w ∈W }. [A] = { B ∈ V ∗d | B = τv (A) for some v ∈ Z } is the equivalence class of arrays with respect to linear translations containing A. The set of all equivalence

@inproceedings{Fernau2013ArrayIA,
title={Array Insertion and Deletion P Systems},
author={Henning Fernau and Rudolf Freund and Sergiu Ivanov and Markus L. Schmid and K. G. Subramanian},
booktitle={UCNC},
year={2013}
}