{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,9]],"date-time":"2025-09-09T21:35:21Z","timestamp":1757453721632,"version":"3.41.2"},"reference-count":0,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","license":[{"start":{"date-parts":[[2019,2,22]],"date-time":"2019-02-22T00:00:00Z","timestamp":1550793600000},"content-version":"am","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2019,2,22]],"date-time":"2019-02-22T00:00:00Z","timestamp":1550793600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2019,2,22]],"date-time":"2019-02-22T00:00:00Z","timestamp":1550793600000},"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":[[2025,3,31]]},"abstract":"<jats:p>It is well known that the length of a beta-reduction sequence of a simply typed lambda-term of order k can be huge; it is as large as k-fold exponential in the size of the lambda-term in the worst case. We consider the following relevant question about quantitative properties, instead of the worst case: how many simply typed lambda-terms have very long reduction sequences? We provide a partial answer to this question, by showing that asymptotically almost every simply typed lambda-term of order k has a reduction sequence as long as (k-1)-fold exponential in the term size, under the assumption that the arity of functions and the number of variables that may occur in every subterm are bounded above by a constant. To prove it, we have extended the infinite monkey theorem for strings to a parametrized one for regular tree languages, which may be of independent interest. The work has been motivated by quantitative analysis of the complexity of higher-order model checking.<\/jats:p>","DOI":"10.23638\/lmcs-15(1:16)2019","type":"journal-article","created":{"date-parts":[[2025,4,3]],"date-time":"2025-04-03T17:36:06Z","timestamp":1743701766000},"source":"Crossref","is-referenced-by-count":1,"title":["Almost Every Simply Typed Lambda-Term Has a Long Beta-Reduction Sequence"],"prefix":"10.23638","volume":"Volume 15, Issue 1","author":[{"given":"Kazuyuki","family":"Asada","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0537-0604","authenticated-orcid":false,"given":"Naoki","family":"Kobayashi","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8152-998X","authenticated-orcid":false,"given":"Ryoma","family":"Sin'ya","sequence":"additional","affiliation":[]},{"given":"Takeshi","family":"Tsukada","sequence":"additional","affiliation":[]}],"member":"25203","published-online":{"date-parts":[[2019,2,22]]},"container-title":["Logical Methods in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/arxiv.org\/pdf\/1801.03886v5","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/arxiv.org\/pdf\/1801.03886v5","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,4,3]],"date-time":"2025-04-03T17:36:07Z","timestamp":1743701767000},"score":1,"resource":{"primary":{"URL":"http:\/\/lmcs.episciences.org\/4203"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,2,22]]},"references-count":0,"URL":"https:\/\/doi.org\/10.23638\/lmcs-15(1:16)2019","relation":{"has-preprint":[{"id-type":"arxiv","id":"1801.03886v3","asserted-by":"subject"},{"id-type":"arxiv","id":"1801.03886v2","asserted-by":"subject"}],"is-same-as":[{"id-type":"arxiv","id":"1801.03886","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.1801.03886","asserted-by":"subject"}]},"ISSN":["1860-5974"],"issn-type":[{"type":"electronic","value":"1860-5974"}],"subject":[],"published":{"date-parts":[[2019,2,22]]},"article-number":"4203"}}