{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T15:39:34Z","timestamp":1753889974489,"version":"3.41.2"},"reference-count":1,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","license":[{"start":{"date-parts":[[2015,12,29]],"date-time":"2015-12-29T00:00:00Z","timestamp":1451347200000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/arxiv.org\/licenses\/nonexclusive-distrib\/1.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"abstract":"<jats:p>We provide elementary algorithms for two preservation theorems for\nfirst-order sentences (FO) on the class \\^ad of all finite structures of degree\nat most d: For each FO-sentence that is preserved under extensions\n(homomorphisms) on \\^ad, a \\^ad-equivalent existential (existential-positive)\nFO-sentence can be constructed in 5-fold (4-fold) exponential time. This is\ncomplemented by lower bounds showing that a 3-fold exponential blow-up of the\ncomputed existential (existential-positive) sentence is unavoidable. Both\nalgorithms can be extended (while maintaining the upper and lower bounds on\ntheir time complexity) to input first-order sentences with modulo m counting\nquantifiers (FO+MODm). Furthermore, we show that for an input FO-formula, a\n\\^ad-equivalent Feferman-Vaught decomposition can be computed in 3-fold\nexponential time. We also provide a matching lower bound.<\/jats:p>","DOI":"10.2168\/lmcs-11(4:17)2015","type":"journal-article","created":{"date-parts":[[2016,11,21]],"date-time":"2016-11-21T13:46:40Z","timestamp":1479736000000},"source":"Crossref","is-referenced-by-count":1,"title":["Preservation and decomposition theorems for bounded degree structures"],"prefix":"10.46298","volume":"Volume 11, Issue 4","author":[{"given":"Frederik","family":"Harwath","sequence":"first","affiliation":[]},{"given":"Lucas","family":"Heimberg","sequence":"additional","affiliation":[]},{"given":"Nicole","family":"Schweikardt","sequence":"additional","affiliation":[]}],"member":"25203","published-online":{"date-parts":[[2015,12,29]]},"reference":[{"key":"1161:not-found"}],"container-title":["Logical Methods in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/lmcs.episciences.org\/1618\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/lmcs.episciences.org\/1618\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,4,11]],"date-time":"2023-04-11T20:08:01Z","timestamp":1681243681000},"score":1,"resource":{"primary":{"URL":"https:\/\/lmcs.episciences.org\/1618"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,12,29]]},"references-count":1,"URL":"https:\/\/doi.org\/10.2168\/lmcs-11(4:17)2015","relation":{"is-same-as":[{"id-type":"arxiv","id":"1511.05888","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.1511.05888","asserted-by":"subject"}]},"ISSN":["1860-5974"],"issn-type":[{"type":"electronic","value":"1860-5974"}],"subject":[],"published":{"date-parts":[[2015,12,29]]},"article-number":"1618"}}