Block invariance and reversibility of one dimensional linear cellular automata
MacLean
S
author
Montalva-Medel
M
author
Goles
E
author
2019
English
Consider a one-dimensional, binary cellular automaton f (the CA rule), where its n nodes are updated according to a deterministic block update (blocks that group all the nodes and such that its order is given by the order of the blocks from left to right and nodes inside a block are updated synchronously). A CA rule is block invariant over a family F of block updates if its set of periodic points does not change, whatever the block update of F is considered. In this work, we study the block invariance of linear CA rules by means of the property of reversibility of the automaton because such a property implies that every configuration has a unique predecessor, so, it is periodic. Specifically, we extend the study of reversibility done for the Wolfram elementary CA rules 90 and 150 as well as, we analyze the reversibility of linear rules with neighbourhood radius 2 by using matrix algebra techniques. (C) 2019 Elsevier Inc. All rights reserved.
Cellular automata
Linear cellular automata
Block invariance
Reversibility
WOS:000459528000004
exported from refbase (show.php?record=983), last updated on Fri, 31 May 2019 21:57:44 -0400
text
10.1016/j.aam.2019.01.003
MacLean_etal2019
Advances In Applied Mathematics
Adv. Appl. Math.
2019
Academic Press Inc Elsevier Science
continuing
periodical
academic journal
105
83
101
0196-8858