{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:53:17Z","timestamp":1753894397999,"version":"3.41.2"},"reference-count":0,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"abstract":"<jats:p>Semi-unification is the combination of first-order unification and\nfirst-order matching. The undecidability of semi-unification has been proven by\nKfoury, Tiuryn, and Urzyczyn in the 1990s by Turing reduction from Turing\nmachine immortality (existence of a diverging configuration). The particular\nTuring reduction is intricate, uses non-computational principles, and involves\nvarious intermediate models of computation. The present work gives a\nconstructive many-one reduction from the Turing machine halting problem to\nsemi-unification. This establishes RE-completeness of semi-unification under\nmany-one reductions. Computability of the reduction function, constructivity of\nthe argument, and correctness of the argument is witnessed by an axiom-free\nmechanization in the Coq proof assistant. Arguably, this serves as\ncomprehensive, precise, and surveyable evidence for the result at hand. The\nmechanization is incorporated into the existing, well-maintained Coq library of\nundecidability proofs. Notably, a variant of Hooper's argument for the\nundecidability of Turing machine immortality is part of the mechanization.<\/jats:p>","DOI":"10.46298\/lmcs-19(4:22)2023","type":"journal-article","created":{"date-parts":[[2023,12,10]],"date-time":"2023-12-10T22:10:10Z","timestamp":1702246210000},"source":"Crossref","is-referenced-by-count":0,"title":["Constructive Many-one Reduction from the Halting Problem to Semi-unification (Extended Version)"],"prefix":"10.46298","volume":"Volume 19, Issue 4","author":[{"given":"Andrej","family":"Dudenhefner","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"25203","published-online":{"date-parts":[[2023,12,8]]},"container-title":["Logical Methods in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/lmcs.episciences.org\/12672\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/lmcs.episciences.org\/12672\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,12,10]],"date-time":"2023-12-10T22:10:10Z","timestamp":1702246210000},"score":1,"resource":{"primary":{"URL":"https:\/\/lmcs.episciences.org\/9977"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,12,8]]},"references-count":0,"URL":"https:\/\/doi.org\/10.46298\/lmcs-19(4:22)2023","relation":{"has-preprint":[{"id-type":"arxiv","id":"2208.13428v3","asserted-by":"subject"},{"id-type":"arxiv","id":"2208.13428v2","asserted-by":"subject"},{"id-type":"arxiv","id":"2208.13428v1","asserted-by":"subject"}],"is-same-as":[{"id-type":"arxiv","id":"2208.13428","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.2208.13428","asserted-by":"subject"}]},"ISSN":["1860-5974"],"issn-type":[{"type":"electronic","value":"1860-5974"}],"subject":[],"published":{"date-parts":[[2023,12,8]]},"article-number":"9977"}}