{"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":1753894406728,"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":[[2025,1,30]]},"abstract":"<jats:p>Every language recognized by a non-deterministic finite automaton can be recognized by a deterministic automaton, at the cost of a potential increase of the number of states, which in the worst case can go from $n$ states to $2^n$ states. In this article, we investigate this classical result in a probabilistic setting where we take a deterministic automaton with $n$ states uniformly at random and add just one random transition. These automata are almost deterministic in the sense that only one state has a non-deterministic choice when reading an input letter. In our model, each state has a fixed probability to be final. We prove that for any $d\\geq 1$, with non-negligible probability the minimal (deterministic) automaton of the language recognized by such an automaton has more than $n^d$ states; as a byproduct, the expected size of its minimal automaton grows faster than any polynomial. Our result also holds when each state is final with some probability that depends on $n$, as long as it is not too close to $0$ and $1$, at distance at least $\\Omega(\\frac1{\\sqrt{n}})$ to be precise, therefore allowing models with a sublinear number of final states in expectation.<\/jats:p>","DOI":"10.46298\/lmcs-21(1:11)2025","type":"journal-article","created":{"date-parts":[[2025,1,30]],"date-time":"2025-01-30T12:50:08Z","timestamp":1738241408000},"source":"Crossref","is-referenced-by-count":0,"title":["Random Deterministic Automata With One Added Transition"],"prefix":"10.46298","volume":"Volume 21, Issue 1","author":[{"given":"Arnaud","family":"Carayol","sequence":"first","affiliation":[]},{"given":"Philippe","family":"Duchon","sequence":"additional","affiliation":[]},{"given":"Florent","family":"Koechlin","sequence":"additional","affiliation":[]},{"given":"Cyril","family":"Nicaud","sequence":"additional","affiliation":[]}],"member":"25203","published-online":{"date-parts":[[2025,1,30]]},"container-title":["Logical Methods in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/lmcs.episciences.org\/15166\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/lmcs.episciences.org\/15166\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,1,30]],"date-time":"2025-01-30T12:50:08Z","timestamp":1738241408000},"score":1,"resource":{"primary":{"URL":"https:\/\/lmcs.episciences.org\/13044"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,1,30]]},"references-count":0,"URL":"https:\/\/doi.org\/10.46298\/lmcs-21(1:11)2025","relation":{"has-preprint":[{"id-type":"arxiv","id":"2402.06591v2","asserted-by":"subject"},{"id-type":"arxiv","id":"2402.06591v1","asserted-by":"subject"}],"is-same-as":[{"id-type":"arxiv","id":"2402.06591","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.2402.06591","asserted-by":"subject"}]},"ISSN":["1860-5974"],"issn-type":[{"type":"electronic","value":"1860-5974"}],"subject":[],"published":{"date-parts":[[2025,1,30]]},"article-number":"13044"}}