{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T15:42:09Z","timestamp":1753890129910,"version":"3.41.2"},"reference-count":0,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","license":[{"start":{"date-parts":[[2019,9,20]],"date-time":"2019-09-20T00:00:00Z","timestamp":1568937600000},"content-version":"am","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2019,9,20]],"date-time":"2019-09-20T00:00:00Z","timestamp":1568937600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2019,9,20]],"date-time":"2019-09-20T00:00:00Z","timestamp":1568937600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100000780","name":"European Commission","doi-asserted-by":"crossref","award":["648276"],"award-info":[{"award-number":["648276"]}],"id":[{"id":"10.13039\/501100000780","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"accepted":{"date-parts":[[2025,3,31]]},"abstract":"<jats:p>The parameterized model-checking problem for a class of first-order sentences (queries) asks to decide whether a given sentence from the class holds true in a given relational structure (database); the parameter is the length of the sentence. We study the parameterized space complexity of the model-checking problem for queries with a bounded number of variables. For each bound on the quantifier alternation rank the problem becomes complete for the corresponding level of what we call the tree hierarchy, a hierarchy of parameterized complexity classes defined via space bounded alternating machines between parameterized logarithmic space and fixed-parameter tractable time. We observe that a parameterized logarithmic space model-checker for existential bounded variable queries would allow to improve Savitch's classical simulation of nondeterministic logarithmic space in deterministic space $O(\\log^2n)$. Further, we define a highly space efficient model-checker for queries with a bounded number of variables and bounded quantifier alternation rank. We study its optimality under the assumption that Savitch's Theorem is optimal.<\/jats:p>","DOI":"10.23638\/lmcs-15(3:31)2019","type":"journal-article","created":{"date-parts":[[2025,4,3]],"date-time":"2025-04-03T17:31:05Z","timestamp":1743701465000},"source":"Crossref","is-referenced-by-count":0,"title":["The parameterized space complexity of model-checking bounded variable first-order logic"],"prefix":"10.23638","volume":"Volume 15, Issue 3","author":[{"given":"Yijia","family":"Chen","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Michael","family":"Elberfeld","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Moritz","family":"M\u00fcller","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"25203","published-online":{"date-parts":[[2019,9,20]]},"container-title":["Logical Methods in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/arxiv.org\/pdf\/1703.01860v6","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/arxiv.org\/pdf\/1703.01860v6","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,4,3]],"date-time":"2025-04-03T17:31:05Z","timestamp":1743701465000},"score":1,"resource":{"primary":{"URL":"http:\/\/lmcs.episciences.org\/3172"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,9,20]]},"references-count":0,"URL":"https:\/\/doi.org\/10.23638\/lmcs-15(3:31)2019","relation":{"has-preprint":[{"id-type":"arxiv","id":"1703.01860v5","asserted-by":"subject"},{"id-type":"arxiv","id":"1703.01860v4","asserted-by":"subject"},{"id-type":"arxiv","id":"1703.01860v3","asserted-by":"subject"},{"id-type":"arxiv","id":"1703.01860v2","asserted-by":"subject"},{"id-type":"arxiv","id":"1703.01860v1","asserted-by":"subject"}],"is-same-as":[{"id-type":"arxiv","id":"1703.01860","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.1703.01860","asserted-by":"subject"}]},"ISSN":["1860-5974"],"issn-type":[{"type":"electronic","value":"1860-5974"}],"subject":[],"published":{"date-parts":[[2019,9,20]]},"article-number":"3172"}}