{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,19]],"date-time":"2025-09-19T09:10:34Z","timestamp":1758273034710,"version":"3.41.2"},"reference-count":1,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","license":[{"start":{"date-parts":[[2015,9,17]],"date-time":"2015-09-17T00:00:00Z","timestamp":1442448000000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/arxiv.org\/licenses\/nonexclusive-distrib\/1.0"}],"funder":[{"DOI":"10.13039\/501100000780","name":"European Commission","doi-asserted-by":"crossref","award":["279499"],"award-info":[{"award-number":["279499"]}],"id":[{"id":"10.13039\/501100000780","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"abstract":"<jats:p>A weighted automaton is functional if any two accepting runs on the same\nfinite word have the same value. In this paper, we investigate functional\nweighted automata for four different measures: the sum, the mean, the\ndiscounted sum of weights along edges and the ratio between rewards and costs.\nOn the positive side, we show that functionality is decidable for the four\nmeasures. Furthermore, the existential and universal threshold problems, the\nlanguage inclusion problem and the equivalence problem are all decidable when\nthe weighted automata are functional. On the negative side, we also study the\nquantitative extension of the realizability problem and show that it is\nundecidable for sum, mean and ratio. We finally show how to decide whether the\nlanguage associated with a given functional automaton can be defined with a\ndeterministic one, for sum, mean and discounted sum. The results on\nfunctionality and determinizability are expressed for the more general class of\nfunctional group automata. This allows one to formulate within the same\nframework new results related to discounted sum automata and known results on\nsum and mean automata. Ratio automata do not fit within this general scheme and\ndifferent techniques are required to decide functionality.<\/jats:p>","DOI":"10.2168\/lmcs-11(3:14)2015","type":"journal-article","created":{"date-parts":[[2016,11,21]],"date-time":"2016-11-21T13:46:02Z","timestamp":1479735962000},"source":"Crossref","is-referenced-by-count":8,"title":["Quantitative Languages Defined by Functional Automata"],"prefix":"10.46298","volume":"Volume 11, Issue 3","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2520-5630","authenticated-orcid":false,"given":"Emmanuel","family":"Filiot","sequence":"first","affiliation":[]},{"given":"Raffaella","family":"Gentilini","sequence":"additional","affiliation":[]},{"given":"Jean-Fran\u00c3\u00a7ois","family":"Raskin","sequence":"additional","affiliation":[]}],"member":"25203","published-online":{"date-parts":[[2015,9,17]]},"reference":[{"key":"1074:not-found"}],"container-title":["Logical Methods in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/lmcs.episciences.org\/1590\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/lmcs.episciences.org\/1590\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,4,11]],"date-time":"2023-04-11T20:07:21Z","timestamp":1681243641000},"score":1,"resource":{"primary":{"URL":"https:\/\/lmcs.episciences.org\/1590"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,9,17]]},"references-count":1,"URL":"https:\/\/doi.org\/10.2168\/lmcs-11(3:14)2015","relation":{"is-same-as":[{"id-type":"arxiv","id":"1111.0862","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.1111.0862","asserted-by":"subject"}]},"ISSN":["1860-5974"],"issn-type":[{"type":"electronic","value":"1860-5974"}],"subject":[],"published":{"date-parts":[[2015,9,17]]},"article-number":"1590"}}