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Author MacLean, S.; Montalva-Medel, M.; Goles, E. doi  openurl
  Title Block invariance and reversibility of one dimensional linear cellular automata Type
  Year 2019 Publication Advances In Applied Mathematics Abbreviated Journal Adv. Appl. Math.  
  Volume 105 Issue Pages 83-101  
  Keywords Cellular automata; Linear cellular automata; Block invariance; Reversibility  
  Abstract 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.  
  Address [MacLean, Stephanie; Montalva-Medel, Marco; Goles, Eric] Univ Adolfo Ibanez, Fac Ingn & Ciencias, Diagonal Torres 2640, Penalolen, Chile, Email: stephanie.macleank@edu.uai.cl;  
  Corporate Author Thesis  
  Publisher Academic Press Inc Elsevier Science Place of Publication Editor  
  Language English Summary Language Original Title  
  Series Editor Series Title Abbreviated Series Title  
  Series Volume Series Issue Edition  
  ISSN 0196-8858 ISBN Medium  
  Area Expedition Conference  
  Notes WOS:000459528000004 Approved  
  Call Number UAI @ eduardo.moreno @ Serial 983  
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Author Goles, E.; Montalva-Medel, M.; MacLean, S.; Mortveit, H. url  openurl
  Title Block Invariance in a Family of Elementary Cellular Automata Type
  Year 2018 Publication Journal Of Cellular Automata Abbreviated Journal J. Cell. Autom.  
  Volume 13 Issue 1-2 Pages 15-32  
  Keywords Elementary cellular automata; block updates; periodic configurations; block invariance  
  Abstract We study the steady state invariance of elementary cellular automata (ECA) under different deterministic updating schemes. Specifically, we study a family of eleven ECA whose steady state invariance were left under conjecture in [2].  
  Address [Goles, Eric; Montalva-Medel, Marco; MacLean, Stephanie] Univ Adolfo Ibanez, Fac Ingn & Ciencias, Santiago, Chile, Email: eric.chacc@uai.cl;  
  Corporate Author Thesis  
  Publisher Old City Publishing Inc Place of Publication Editor  
  Language English Summary Language Original Title  
  Series Editor Series Title Abbreviated Series Title  
  Series Volume Series Issue Edition  
  ISSN 1557-5969 ISBN Medium  
  Area Expedition Conference  
  Notes WOS:000410888100002 Approved  
  Call Number UAI @ eduardo.moreno @ Serial 782  
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