{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,19]],"date-time":"2026-06-19T18:16:11Z","timestamp":1781892971882,"version":"3.54.5"},"reference-count":0,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","license":[{"start":{"date-parts":[[2007,5,4]],"date-time":"2007-05-04T00:00:00Z","timestamp":1178236800000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/arxiv.org\/licenses\/assumed-1991-2003"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"abstract":"<jats:p>We consider a new kind of interpretation over relational structures: finite\nsets interpretations. Those interpretations are defined by weak monadic\nsecond-order (WMSO) formulas with free set variables. They transform a given\nstructure into a structure with a domain consisting of finite sets of elements\nof the orignal structure. The definition of these interpretations directly\nimplies that they send structures with a decidable WMSO theory to structures\nwith a decidable first-order theory. In this paper, we investigate the\nexpressive power of such interpretations applied to infinite deterministic\ntrees. The results can be used in the study of automatic and tree-automatic\nstructures.<\/jats:p>","DOI":"10.2168\/lmcs-3(2:4)2007","type":"journal-article","created":{"date-parts":[[2008,6,3]],"date-time":"2008-06-03T12:00:52Z","timestamp":1212494452000},"source":"Crossref","is-referenced-by-count":20,"title":["Transforming structures by set interpretations"],"prefix":"10.46298","volume":"Volume 3, Issue 2","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6529-6963","authenticated-orcid":false,"given":"Thomas","family":"Colcombet","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Christof","family":"L\u00f6ding","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"25203","published-online":{"date-parts":[[2007,5,4]]},"container-title":["Logical Methods in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/lmcs.episciences.org\/2221\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/lmcs.episciences.org\/2221\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,4,11]],"date-time":"2023-04-11T20:09:48Z","timestamp":1681243788000},"score":1,"resource":{"primary":{"URL":"https:\/\/lmcs.episciences.org\/2221"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2007,5,4]]},"references-count":0,"URL":"https:\/\/doi.org\/10.2168\/lmcs-3(2:4)2007","relation":{"is-same-as":[{"id-type":"arxiv","id":"cs\/0703039","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.cs\/0703039","asserted-by":"subject"}],"is-referenced-by":[{"id-type":"arxiv","id":"0810.4998","asserted-by":"subject"},{"id-type":"doi","id":"10.1007\/978-3-642-04027-6_27","asserted-by":"subject"},{"id-type":"doi","id":"10.2178\/jsl\/1318338854","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arxiv.0810.4998","asserted-by":"subject"}]},"ISSN":["1860-5974"],"issn-type":[{"value":"1860-5974","type":"electronic"}],"subject":[],"published":{"date-parts":[[2007,5,4]]},"article-number":"2221"}}