{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T15:38:59Z","timestamp":1753889939124,"version":"3.41.2"},"reference-count":0,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","license":[{"start":{"date-parts":[[2019,12,19]],"date-time":"2019-12-19T00:00:00Z","timestamp":1576713600000},"content-version":"am","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2019,12,19]],"date-time":"2019-12-19T00:00:00Z","timestamp":1576713600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2019,12,19]],"date-time":"2019-12-19T00:00:00Z","timestamp":1576713600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100001665","name":"French National Research Agency","doi-asserted-by":"crossref","award":["ANR-13-JS02-0010"],"award-info":[{"award-number":["ANR-13-JS02-0010"]}],"id":[{"id":"10.13039\/501100001665","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"accepted":{"date-parts":[[2025,3,31]]},"abstract":"<jats:p>Rational word languages can be defined by several equivalent means: finite state automata, rational expressions, finite congruences, or monadic second-order (MSO) logic. The robust subclass of aperiodic languages is defined by: counter-free automata, star-free expressions, aperiodic (finite) congruences, or first-order (FO) logic. In particular, their algebraic characterization by aperiodic congruences allows to decide whether a regular language is aperiodic.   We lift this decidability result to rational transductions, i.e., word-to-word functions defined by finite state transducers. In this context, logical and algebraic characterizations have also been proposed. Our main result is that one can decide if a rational transduction (given as a transducer) is in a given decidable congruence class. We also establish a transfer result from logic-algebra equivalences over languages to equivalences over transductions. As a consequence, it is decidable if a rational transduction is first-order definable, and we show that this problem is PSPACE-complete.<\/jats:p>","DOI":"10.23638\/lmcs-15(4:16)2019","type":"journal-article","created":{"date-parts":[[2025,4,3]],"date-time":"2025-04-03T17:32:00Z","timestamp":1743701520000},"source":"Crossref","is-referenced-by-count":0,"title":["Logical and Algebraic Characterizations of Rational Transductions"],"prefix":"10.23638","volume":"Volume 15, Issue 4","author":[{"given":"Emmanuel","family":"Filiot","sequence":"first","affiliation":[]},{"given":"Olivier","family":"Gauwin","sequence":"additional","affiliation":[]},{"given":"Nathan","family":"Lhote","sequence":"additional","affiliation":[]}],"member":"25203","published-online":{"date-parts":[[2019,12,19]]},"container-title":["Logical Methods in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/arxiv.org\/pdf\/1705.03726v5","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/arxiv.org\/pdf\/1705.03726v5","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,4,3]],"date-time":"2025-04-03T17:32:00Z","timestamp":1743701520000},"score":1,"resource":{"primary":{"URL":"http:\/\/lmcs.episciences.org\/3653"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,12,19]]},"references-count":0,"URL":"https:\/\/doi.org\/10.23638\/lmcs-15(4:16)2019","relation":{"has-preprint":[{"id-type":"arxiv","id":"1705.03726v4","asserted-by":"subject"},{"id-type":"arxiv","id":"1705.03726v3","asserted-by":"subject"},{"id-type":"arxiv","id":"1705.03726v2","asserted-by":"subject"},{"id-type":"arxiv","id":"1705.03726v1","asserted-by":"subject"}],"is-same-as":[{"id-type":"arxiv","id":"1705.03726","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.1705.03726","asserted-by":"subject"}]},"ISSN":["1860-5974"],"issn-type":[{"type":"electronic","value":"1860-5974"}],"subject":[],"published":{"date-parts":[[2019,12,19]]},"article-number":"3653"}}