{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T15:41:12Z","timestamp":1753890072425,"version":"3.41.2"},"reference-count":0,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","license":[{"start":{"date-parts":[[2019,10,29]],"date-time":"2019-10-29T00:00:00Z","timestamp":1572307200000},"content-version":"am","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2019,10,29]],"date-time":"2019-10-29T00:00:00Z","timestamp":1572307200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2019,10,29]],"date-time":"2019-10-29T00:00:00Z","timestamp":1572307200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"accepted":{"date-parts":[[2025,3,31]]},"abstract":"<jats:p>We study varieties of certain ordered $\\Sigma$-algebras with restricted completeness and continuity properties. We give a general characterization of their free algebras in terms of submonads of the monad of $\\Sigma$-coterms. Varieties of this form are called \\emph{quasi-regular}. For example, we show that if $E$ is a set of inequalities between finite $\\Sigma$-terms, and if $\\mathcal{V}_\\omega$ and $\\mathcal{V}_\\mathrm{reg}$ denote the varieties of all $\\omega$-continuous ordered $\\Sigma$-algebras and regular ordered $\\Sigma$-algebras satisfying $E$, respectively, then the free $\\mathcal{V}_\\mathrm{reg}$-algebra $F_\\mathrm{reg}(X)$ on generators $X$ is the subalgebra of the corresponding free $\\mathcal{V}_\\omega$-algebra $F_\\omega(X)$ determined by those elements of $F_\\omega(X)$ denoted by the regular $\\Sigma$-coterms. This is a special case of a more general construction that applies to any quasi-regular family. Examples include the *-continuous Kleene algebras, context-free languages, $\\omega$-continuous semirings and $\\omega$-continuous idempotent semirings, OI-macro languages, and iteration theories.<\/jats:p>","DOI":"10.23638\/lmcs-15(4:4)2019","type":"journal-article","created":{"date-parts":[[2025,4,3]],"date-time":"2025-04-03T17:29:13Z","timestamp":1743701353000},"source":"Crossref","is-referenced-by-count":0,"title":["On Free $\\omega$-Continuous and Regular Ordered Algebras"],"prefix":"10.23638","volume":"Volume 15, Issue 4","author":[{"given":"Zoltan","family":"Esik","sequence":"first","affiliation":[]},{"given":"Dexter","family":"Kozen","sequence":"additional","affiliation":[]}],"member":"25203","published-online":{"date-parts":[[2019,10,29]]},"container-title":["Logical Methods in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/arxiv.org\/pdf\/1612.02106v5","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/arxiv.org\/pdf\/1612.02106v5","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,4,3]],"date-time":"2025-04-03T17:29:13Z","timestamp":1743701353000},"score":1,"resource":{"primary":{"URL":"http:\/\/lmcs.episciences.org\/2586"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,10,29]]},"references-count":0,"URL":"https:\/\/doi.org\/10.23638\/lmcs-15(4:4)2019","relation":{"has-preprint":[{"id-type":"arxiv","id":"1612.02106v4","asserted-by":"subject"},{"id-type":"arxiv","id":"1612.02106v3","asserted-by":"subject"},{"id-type":"arxiv","id":"1612.02106v2","asserted-by":"subject"},{"id-type":"arxiv","id":"1612.02106v1","asserted-by":"subject"}],"is-same-as":[{"id-type":"arxiv","id":"1612.02106","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.1612.02106","asserted-by":"subject"}]},"ISSN":["1860-5974"],"issn-type":[{"type":"electronic","value":"1860-5974"}],"subject":[],"published":{"date-parts":[[2019,10,29]]},"article-number":"2586"}}