{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,5]],"date-time":"2022-04-05T22:55:41Z","timestamp":1649199341329},"reference-count":11,"publisher":"World Scientific Pub Co Pte Lt","issue":"02","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Found. Comput. Sci."],"published-print":{"date-parts":[[2006,4]]},"abstract":" The paper investigates two-dimensional recognizable languages that are defined by the so-called \"dot systems\" that are special subgroups of (\u2124\/2\u2124)\u21242<\/jats:sup><\/jats:sup>. The dot shapes that provide directional transitivity or mixing for the related language are investigated. It is shown that languages defined by parallelogram shapes fail to be transitive in the direction of a defining vector and hence fail to be mixing, while certain triangular shapes guarantee that the factor language of the associated dot system will be mixing. Dot systems belong to a class of two-dimensional shift spaces that have a factor language such that every admissable block can be extended to a configuration of the entire plane. For this class of shift spaces we introduce a finite graph (i.e., a finite state automaton) that recognizes two-dimensional local languages, then show that certain transitivity properties may be observed from the structure of the finite graph. <\/jats:p>","DOI":"10.1142\/s0129054106003917","type":"journal-article","created":{"date-parts":[[2006,4,3]],"date-time":"2006-04-03T09:47:03Z","timestamp":1144057623000},"page":"435-463","source":"Crossref","is-referenced-by-count":6,"title":["TRANSITIVITY IN TWO-DIMENSIONAL LOCAL LANGUAGES DEFINED BY DOT SYSTEMS"],"prefix":"10.1142","volume":"17","author":[{"given":"NATA\u0160A","family":"JONOSKA","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of South Florida, 4202 East Fowler Avenue, Tampa, FL 33620, USA"}]},{"given":"JONI BURNETTE","family":"PIRNOT","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Manatee Community College, 5840 26th Street West, Bradenton, FL 34207, USA"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","series-title":"Memoirs AMS no. 66","volume-title":"The undecidability of the Domino Problem","author":"Berger R.","year":"1966"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-59126-6_4"},{"key":"rf5","series-title":"AMS Colloquium Pubs","doi-asserted-by":"crossref","DOI":"10.1090\/coll\/036","volume-title":"Topological Dynamics","volume":"36","author":"Gottschalk W. H.","year":"1955"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1016\/0020-0255(91)90008-I"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-99-04678-X"},{"key":"rf12","doi-asserted-by":"crossref","first-page":"691","DOI":"10.1017\/S0143385700005290","volume":"9","author":"Kitchens B.","journal-title":"Ergod. Th. & Dynam. Sys."},{"key":"rf13","doi-asserted-by":"publisher","DOI":"10.1090\/conm\/135\/1185094"},{"key":"rf14","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511626302"},{"key":"rf15","first-page":"251","volume":"43","author":"Markley N.","journal-title":"Proc. London Math. Soc."},{"key":"rf16","doi-asserted-by":"publisher","DOI":"10.2140\/pjm.2001.200.497"},{"key":"rf17","volume-title":"Dynamical systems of algebraic origin","author":"Schmidt K.","year":"1995"}],"container-title":["International Journal of Foundations of Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0129054106003917","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T15:28:45Z","timestamp":1565191725000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0129054106003917"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006,4]]},"references-count":11,"journal-issue":{"issue":"02","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2006,4]]}},"alternative-id":["10.1142\/S0129054106003917"],"URL":"https:\/\/doi.org\/10.1142\/s0129054106003917","relation":{},"ISSN":["0129-0541","1793-6373"],"issn-type":[{"value":"0129-0541","type":"print"},{"value":"1793-6373","type":"electronic"}],"subject":[],"published":{"date-parts":[[2006,4]]}}}