{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:53:26Z","timestamp":1753894406627,"version":"3.41.2"},"reference-count":0,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"accepted":{"date-parts":[[2025,1,31]]},"abstract":"<jats:p>String diagrams are pictorial representations for morphisms of symmetric monoidal categories. They constitute an intuitive and expressive graphical syntax, which has found application in a very diverse range of fields including concurrency theory, quantum computing, control theory, machine learning, linguistics, and digital circuits. Rewriting theory for string diagrams relies on a combinatorial interpretation as double-pushout rewriting of certain hypergraphs. As previously studied, there is a `tension' in this interpretation: in order to make it sound and complete, we either need to add structure on string diagrams (in particular, Frobenius algebra structure) or pose restrictions on double-pushout rewriting (resulting in 'convex' rewriting). From the string diagram viewpoint, imposing a full Frobenius structure may not always be natural or desirable in applications, which motivates our study of a weaker requirement: commutative monoid structure. In this work we characterise string diagram rewriting modulo commutative monoid equations, via a sound and complete interpretation in a suitable notion of double-pushout rewriting of hypergraphs.<\/jats:p>","DOI":"10.46298\/lmcs-21(1:12)2025","type":"journal-article","created":{"date-parts":[[2025,1,31]],"date-time":"2025-01-31T12:10:06Z","timestamp":1738325406000},"source":"Crossref","is-referenced-by-count":1,"title":["Rewriting for Symmetric Monoidal Categories with Commutative (Co)Monoid Structure"],"prefix":"10.46298","volume":"Volume 21, Issue 1","author":[{"given":"Aleksandar","family":"Milosavljevic","sequence":"first","affiliation":[]},{"given":"Robin","family":"Piedeleu","sequence":"additional","affiliation":[]},{"given":"Fabio","family":"Zanasi","sequence":"additional","affiliation":[]}],"member":"25203","published-online":{"date-parts":[[2025,1,31]]},"container-title":["Logical Methods in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/lmcs.episciences.org\/15169\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/lmcs.episciences.org\/15169\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,1,31]],"date-time":"2025-01-31T12:10:07Z","timestamp":1738325407000},"score":1,"resource":{"primary":{"URL":"https:\/\/lmcs.episciences.org\/14937"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,1,31]]},"references-count":0,"URL":"https:\/\/doi.org\/10.46298\/lmcs-21(1:12)2025","relation":{"has-preprint":[{"id-type":"arxiv","id":"2204.04274v3","asserted-by":"subject"}],"is-same-as":[{"id-type":"arxiv","id":"2204.04274","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.2204.04274","asserted-by":"subject"}]},"ISSN":["1860-5974"],"issn-type":[{"type":"electronic","value":"1860-5974"}],"subject":[],"published":{"date-parts":[[2025,1,31]]},"article-number":"14937"}}