{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T06:44:37Z","timestamp":1740120277145,"version":"3.37.3"},"reference-count":21,"publisher":"World Scientific Pub Co Pte Ltd","issue":"06","funder":[{"DOI":"10.13039\/501100001824","name":"Czech Science Foundation","doi-asserted-by":"crossref","award":["18-20123S"],"award-info":[{"award-number":["18-20123S"]}],"id":[{"id":"10.13039\/501100001824","id-type":"DOI","asserted-by":"crossref"}]},{"name":"Charles University Research Center","award":["UNCE\/SCI\/022","PRIMUS\/21\/SCI\/014"],"award-info":[{"award-number":["UNCE\/SCI\/022","PRIMUS\/21\/SCI\/014"]}]},{"name":"Czech Ministry of Education M\u0160MT.","award":["LTAUSA19070"],"award-info":[{"award-number":["LTAUSA19070"]}]},{"name":"European Research Council","award":["714532"],"award-info":[{"award-number":["714532"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2022,9]]},"abstract":"<jats:p> For some Maltsev conditions [Formula: see text] it is enough to check if a finite algebra [Formula: see text] satisfies [Formula: see text] locally on subsets of bounded size in order to decide whether [Formula: see text] satisfies [Formula: see text] (globally). This local\u2013global property is the main known source of tractability results for deciding Maltsev conditions. In this paper, we investigate the local\u2013global property for the existence of a G-term, i.e. an [Formula: see text]-ary term that is invariant under permuting its variables according to a permutation group [Formula: see text]. Our results imply in particular that all cyclic loop conditions (in the sense of Bodirsky, Starke, and Vucaj) have the local\u2013global property (and thus can be decided in polynomial time), while symmetric terms of arity [Formula: see text] fail to have it. <\/jats:p>","DOI":"10.1142\/s0218196722500527","type":"journal-article","created":{"date-parts":[[2022,5,20]],"date-time":"2022-05-20T14:20:48Z","timestamp":1653056448000},"page":"1209-1231","source":"Crossref","is-referenced-by-count":0,"title":["Local\u2013global property for G-invariant terms"],"prefix":"10.1142","volume":"32","author":[{"given":"Alexandr","family":"Kazda","sequence":"first","affiliation":[{"name":"Department of Algebra, Faculty of Mathematics, and Physics, Charles University, Sokolovsk\u00e1 49\/83, 186 75 Praha 8, Czech Republic"}]},{"given":"Michael","family":"Kompatscher","sequence":"additional","affiliation":[{"name":"Department of Algebra, Faculty of Mathematics, and Physics, Charles University, Sokolovsk\u00e1 49\/83, 186 75 Praha 8, Czech Republic"}]}],"member":"219","published-online":{"date-parts":[[2022,6,21]]},"reference":[{"key":"S0218196722500527BIB001","series-title":"LIPIcs","first-page":"11:1","volume-title":"Proc. 46th Int. Symp. Mathematical Foundations of Computer Science","volume":"202","author":"Asimi K.","year":"2021"},{"key":"S0218196722500527BIB002","doi-asserted-by":"publisher","DOI":"10.1007\/s11856-017-1621-9"},{"key":"S0218196722500527BIB003","doi-asserted-by":"publisher","DOI":"10.1201\/9781439851302"},{"key":"S0218196722500527BIB004","doi-asserted-by":"publisher","DOI":"10.1017\/9781107337534"},{"key":"S0218196722500527BIB005","doi-asserted-by":"publisher","DOI":"10.1142\/S0218196721500442"},{"key":"S0218196722500527BIB006","doi-asserted-by":"publisher","DOI":"10.1137\/20M1312745"},{"key":"S0218196722500527BIB007","doi-asserted-by":"publisher","DOI":"10.1145\/3134757"},{"key":"S0218196722500527BIB008","doi-asserted-by":"publisher","DOI":"10.1142\/S021819671950036X"},{"key":"S0218196722500527BIB009","doi-asserted-by":"publisher","DOI":"10.1142\/S0218196709004956"},{"key":"S0218196722500527BIB010","doi-asserted-by":"publisher","DOI":"10.1112\/blms.12286"},{"key":"S0218196722500527BIB011","doi-asserted-by":"publisher","DOI":"10.1090\/conm\/076"},{"key":"S0218196722500527BIB012","doi-asserted-by":"publisher","DOI":"10.1142\/S0218196713500343"},{"key":"S0218196722500527BIB013","doi-asserted-by":"publisher","DOI":"10.24033\/asens.961"},{"issue":"4","key":"S0218196722500527BIB014","first-page":"337","volume":"36","author":"Kazda A.","year":"2021","journal-title":"J. Multiple-Valued Logic Soft Comput."},{"key":"S0218196722500527BIB015","doi-asserted-by":"publisher","DOI":"10.4153\/S0008439519000651"},{"key":"S0218196722500527BIB016","doi-asserted-by":"publisher","DOI":"10.1017\/jsl.2019.73"},{"key":"S0218196722500527BIB017","doi-asserted-by":"publisher","DOI":"10.1142\/S0218196712500750"},{"key":"S0218196722500527BIB018","doi-asserted-by":"publisher","DOI":"10.1142\/S0218196720500083"},{"key":"S0218196722500527BIB019","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-4176-8"},{"key":"S0218196722500527BIB020","series-title":"Graduate Texts in Mathematics","volume-title":"A Course in Universal Algebra","volume":"78","author":"Sankappanavar H. P.","year":"1981"},{"key":"S0218196722500527BIB021","doi-asserted-by":"publisher","DOI":"10.1112\/blms\/bdu044"}],"container-title":["International Journal of Algebra and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218196722500527","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,8,26]],"date-time":"2022-08-26T07:07:44Z","timestamp":1661497664000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/10.1142\/S0218196722500527"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,6,21]]},"references-count":21,"journal-issue":{"issue":"06","published-print":{"date-parts":[[2022,9]]}},"alternative-id":["10.1142\/S0218196722500527"],"URL":"https:\/\/doi.org\/10.1142\/s0218196722500527","relation":{},"ISSN":["0218-1967","1793-6500"],"issn-type":[{"type":"print","value":"0218-1967"},{"type":"electronic","value":"1793-6500"}],"subject":[],"published":{"date-parts":[[2022,6,21]]}}}