{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T15:37:06Z","timestamp":1753889826326,"version":"3.41.2"},"reference-count":0,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","license":[{"start":{"date-parts":[[2020,5,14]],"date-time":"2020-05-14T00:00:00Z","timestamp":1589414400000},"content-version":"am","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2020,5,14]],"date-time":"2020-05-14T00:00:00Z","timestamp":1589414400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2020,5,14]],"date-time":"2020-05-14T00:00:00Z","timestamp":1589414400000},"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":[[2025,4,1]]},"abstract":"<jats:p>In 2008, Ben-Amram, Jones and Kristiansen showed that for a simple programming language - representing non-deterministic imperative programs with bounded loops, and arithmetics limited to addition and multiplication - it is possible to decide precisely whether a program has certain growth-rate properties, in particular whether a computed value, or the program's running time, has a polynomial growth rate.   A natural and intriguing problem was to move from answering the decision problem to giving a quantitative result, namely, a tight polynomial upper bound. This paper shows how to obtain asymptotically-tight, multivariate, disjunctive polynomial bounds for this class of programs. This is a complete solution: whenever a polynomial bound exists it will be found.   A pleasant surprise is that the algorithm is quite simple; but it relies on some subtle reasoning. An important ingredient in the proof is the forest factorization theorem, a strong structural result on homomorphisms into a finite monoid.<\/jats:p>","DOI":"10.23638\/lmcs-16(2:4)2020","type":"journal-article","created":{"date-parts":[[2025,4,3]],"date-time":"2025-04-03T17:45:46Z","timestamp":1743702346000},"source":"Crossref","is-referenced-by-count":0,"title":["Tight Polynomial Worst-Case Bounds for Loop Programs"],"prefix":"10.23638","volume":"Volume 16, Issue 2","author":[{"given":"Amir M.","family":"Ben-Amram","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5954-6444","authenticated-orcid":false,"given":"Geoff","family":"Hamilton","sequence":"additional","affiliation":[]}],"member":"25203","published-online":{"date-parts":[[2020,5,14]]},"container-title":["Logical Methods in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/arxiv.org\/pdf\/1906.10047v5","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/arxiv.org\/pdf\/1906.10047v5","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,4,3]],"date-time":"2025-04-03T17:45:46Z","timestamp":1743702346000},"score":1,"resource":{"primary":{"URL":"http:\/\/lmcs.episciences.org\/5596"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,5,14]]},"references-count":0,"URL":"https:\/\/doi.org\/10.23638\/lmcs-16(2:4)2020","relation":{"has-preprint":[{"id-type":"arxiv","id":"1906.10047v4","asserted-by":"subject"},{"id-type":"arxiv","id":"1906.10047v2","asserted-by":"subject"},{"id-type":"arxiv","id":"1906.10047v1","asserted-by":"subject"}],"is-same-as":[{"id-type":"arxiv","id":"1906.10047","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.1906.10047","asserted-by":"subject"}]},"ISSN":["1860-5974"],"issn-type":[{"type":"electronic","value":"1860-5974"}],"subject":[],"published":{"date-parts":[[2020,5,14]]},"article-number":"5596"}}