{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T15:58:07Z","timestamp":1772294287709,"version":"3.50.1"},"reference-count":7,"publisher":"World Scientific Pub Co Pte Lt","issue":"04","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Advs. Complex Syst."],"published-print":{"date-parts":[[2005,12]]},"abstract":"<jats:p> We study asynchronous cellular automata (ACA) induced by symmetric Boolean functions [1]. These systems can be considered as sequential dynamical systems (SDS) over words, a class of dynamical systems that consists of (a) a finite, labeled graph Y with vertex set {v<jats:sub>1<\/jats:sub>,\u2026,v<jats:sub>n<\/jats:sub>} and where each vertex v<jats:sub>i<\/jats:sub> has a state x<jats:sub>v<jats:sub>i<\/jats:sub><\/jats:sub> in a finite field K, (b) a sequence of functions (F<jats:sub>v<jats:sub>i<\/jats:sub>,Y<\/jats:sub>)<jats:sub>i<\/jats:sub>, and (c) a word w = (w<jats:sub>1<\/jats:sub>,\u2026,w<jats:sub>k<\/jats:sub>), where each w<jats:sub>i<\/jats:sub> is a vertex in Y. The function F<jats:sub>v<jats:sub>i<\/jats:sub>,Y<\/jats:sub> updates the state of vertex v<jats:sub>i<\/jats:sub> as a function of the state of v<jats:sub>i<\/jats:sub> and its Y-neighbors and maps all other vertex states identically. The SDS is the composed map [Formula: see text]. In the particular case of ACA, the graph is the circle graph on n vertices (Y = Circ <jats:sub>n<\/jats:sub>), and all the maps F<jats:sub>v<jats:sub>i<\/jats:sub><\/jats:sub> are induced by a common Boolean function. Our main result is the identification of all w-independent ACA, that is, all ACA with periodic points that are independent of the word (update schedule) w. In general, for each w-independent SDS, there is a finite group whose structure contains information about for example SDS with specific phase space properties. We classify and enumerate the set of periodic points for all w-independent ACA, and we also compute their associated groups in the case of Y = Circ <jats:sub>4<\/jats:sub>. Finally, we analyze invertible ACA and offer an interpretation of S<jats:sub>35<\/jats:sub> as the group of an SDS over the three-dimensional cube with local functions induced by nor<jats:sub>3<\/jats:sub> + nand<jats:sub>3<\/jats:sub>. <\/jats:p>","DOI":"10.1142\/s0219525905000555","type":"journal-article","created":{"date-parts":[[2006,1,5]],"date-time":"2006-01-05T00:48:36Z","timestamp":1136422116000},"page":"521-538","source":"Crossref","is-referenced-by-count":13,"title":["ON ASYNCHRONOUS CELLULAR AUTOMATA"],"prefix":"10.1142","volume":"08","author":[{"given":"A. \u00c5.","family":"HANSSON","sequence":"first","affiliation":[{"name":"Los Alamos National Laboratory, CCS-DSS, 87545 New Mexico, USA"}]},{"given":"H. S.","family":"MORTVEIT","sequence":"additional","affiliation":[{"name":"VBI\/Department of Mathematics, Virgina Polytechnic Institute and State University, Blacksburg, VA 24061, USA"}]},{"given":"C. M.","family":"REIDYS","sequence":"additional","affiliation":[{"name":"Los Alamos National Laboratory, CCS-DSS, 87545 New Mexico, USA"}]}],"member":"219","published-online":{"date-parts":[[2012,3,16]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1016\/S0096-3003(00)00042-4"},{"key":"rf2","series-title":"Lecture Notes in Mathematics","doi-asserted-by":"crossref","DOI":"10.1007\/BFb0079468","volume-title":"Problemes Combinatoires de Commutation et Re\u00e1rrangements","volume":"85","author":"Cartier P.","year":"1969"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4613-0163-9"},{"key":"rf6","series-title":"Bayreuther Mathematische Schriften","volume-title":"Zur konstruktion und klassifikation endlicher aufl\u00f6sbarer gruppen","volume":"9","author":"Laue R.","year":"1982"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.2307\/1968149"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1016\/S0012-365X(00)00115-1"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1006\/aama.2001.0761"}],"container-title":["Advances in Complex Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0219525905000555","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T15:09:30Z","timestamp":1565190570000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0219525905000555"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2005,12]]},"references-count":7,"journal-issue":{"issue":"04","published-online":{"date-parts":[[2012,3,16]]},"published-print":{"date-parts":[[2005,12]]}},"alternative-id":["10.1142\/S0219525905000555"],"URL":"https:\/\/doi.org\/10.1142\/s0219525905000555","relation":{},"ISSN":["0219-5259","1793-6802"],"issn-type":[{"value":"0219-5259","type":"print"},{"value":"1793-6802","type":"electronic"}],"subject":[],"published":{"date-parts":[[2005,12]]}}}