Research Notices The injectivity of the global function of a cellular automaton in the hyperbolic plane is undecidable Maurice Margenstern1 This is the title of a paper which is available on arXiv, see [1] and on the web site of the author, see [2], in an abridged version. The paper deals with the global function of a cellular automaton on the ternary heptagrid, which is the tiling {7, 3} of the hyperbolic plane. The notion of cellular automata in the hyperbolic plane where introduced by the author in several papers referenced in [1, 2]. References to the global function of a cellular automaton in this context are to be found there as well. For CAâs on the Euclidean plane, Jarkko Kari proved in 1994 that the injectivity of the global function of a cellular automaton on the plane is undecidable. In the papers [1, 2], the injectivity of the global function is proved undecidable for cellular automata in the hyperbolic plane, namely on the ternary heptagrid. The proof consists in a two-stage construction, the ï¬rst stage of which is the construction with which the author proved the undecidability of the domino problem in the hyperbolic plane. In fact, the proof can be transported to any tiling {p, 3} of the hyperbolic plane, with p ⥠7. The author is much in debt to the editor for giving him the opportunity to mention this result here.
/lp/association-for-computing-machinery/research-notices-the-injectivity-of-the-global-function-of-a-cellular-SUgh9CZQt0
Welcome to DeepDyve! Rent Premier Research Articles and Save Up to 90%
Free Article
Research Notices: The injectivity of the global function of a cellular automaton in the hyperbolic plane is undecidable
Margenstern, Maurice
Follow ACM SIGACT News
, Volume 39 (3)
Association for Computing Machinery – Sep 1, 2008
More Info
More Like This Article
View All dataSource[]=actageo&dataSource[]=aspet&dataSource[]=aaos&dataSource[]=aacc&dataSource[]=aacr&dataSource[]=aea&dataSource[]=aip&dataSource[]=ajnr&dataSource[]=ams&dataSource[]=aps_physical&dataSource[]=appi_book&dataSource[]=appi_journal&dataSource[]=apha&dataSource[]=asip&dataSource[]=asm&dataSource[]=asn&dataSource[]=aspb&dataSource[]=avs&dataSource[]=annual_reviews&dataSource[]=arxiv&dataSource[]=acm&dataSource[]=berghahn&dataSource[]=cabi&dataSource[]=clinical_trials&dataSource[]=dailymed&dataSource[]=degruyter&dataSource[]=du_press&dataSource[]=esa&dataSource[]=eu_press&dataSource[]=elsevier&dataSource[]=emerald&dataSource[]=ejtr&dataSource[]=emea&dataSource[]=epo&dataSource[]=faseb&dataSource[]=gsa&dataSource[]=health_affairs&dataSource[]=hindawi&dataSource[]=imanager&dataSource[]=imedpub&dataSource[]=informa_healthcare&dataSource[]=informs&dataSource[]=iop&dataSource[]=iucr&dataSource[]=iospress&dataSource[]=jbjs&dataSource[]=leftcoast&dataSource[]=lu_press&dataSource[]=mesharpe&dataSource[]=mary_ann_liebert&dataSource[]=medline&dataSource[]=mit_press&dataSource[]=nature&dataSource[]=oxford&dataSource[]=pier_professional&dataSource[]=pnas&dataSource[]=portlandpress&dataSource[]=psyc_articles&dataSource[]=psyc_books&dataSource[]=psyc_critiques&dataSource[]=plos_journal&dataSource[]=pubmed_central&dataSource[]=rsna&dataSource[]=rockefeller&dataSource[]=rcn&dataSource[]=ria&dataSource[]=rsc&dataSource[]=sage&dataSource[]=spie&dataSource[]=springer_journal&dataSource[]=springer&dataSource[]=taylor_francis&dataSource[]=aps&dataSource[]=the_scientist&dataSource[]=uc_press&dataSource[]=uspto_abstract&dataSource[]=wiley&dataSource[]=pct
© 2012 DeepDyve, Inc. All rights reserved.
Terms of Service | Privacy Policy
