{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,11]],"date-time":"2026-02-11T14:04:13Z","timestamp":1770818653375,"version":"3.50.1"},"reference-count":1,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","license":[{"start":{"date-parts":[[2014,9,10]],"date-time":"2014-09-10T00:00:00Z","timestamp":1410307200000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/arxiv.org\/licenses\/nonexclusive-distrib\/1.0"}],"funder":[{"name":"National Science Foundation","award":["1001847"],"award-info":[{"award-number":["1001847"]}]},{"name":"National Science Foundation","award":["1266214"],"award-info":[{"award-number":["1266214"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"abstract":"<jats:p>We investigate the truth-table degrees of (co-)c.e.\\ sets, in particular,\nsets of random strings. It is known that the set of random strings with respect\nto any universal prefix-free machine is Turing complete, but that truth-table\ncompleteness depends on the choice of universal machine. We show that for such\nsets of random strings, any finite set of their truth-table degrees do not meet\nto the degree~0, even within the c.e. truth-table degrees, but when taking the\nmeet over all such truth-table degrees, the infinite meet is indeed~0. The\nlatter result proves a conjecture of Allender, Friedman and Gasarch. We also\nshow that there are two Turing complete c.e. sets whose truth-table degrees\nform a minimal pair.<\/jats:p>","DOI":"10.2168\/lmcs-10(3:15)2014","type":"journal-article","created":{"date-parts":[[2014,11,14]],"date-time":"2014-11-14T09:40:57Z","timestamp":1415958057000},"source":"Crossref","is-referenced-by-count":5,"title":["Random strings and tt-degrees of Turing complete C.E. sets"],"prefix":"10.46298","volume":"Volume 10, Issue 3","author":[{"given":"Mingzhong","family":"Cai","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Rodney G","family":"Downey","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Rachel","family":"Epstein","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Steffen","family":"Lempp","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Joseph","family":"Miller","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"25203","published-online":{"date-parts":[[2014,9,10]]},"reference":[{"key":"993:not-found"}],"container-title":["Logical Methods in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/lmcs.episciences.org\/1126\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/lmcs.episciences.org\/1126\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,4,11]],"date-time":"2023-04-11T20:04:16Z","timestamp":1681243456000},"score":1,"resource":{"primary":{"URL":"https:\/\/lmcs.episciences.org\/1126"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,9,10]]},"references-count":1,"URL":"https:\/\/doi.org\/10.2168\/lmcs-10(3:15)2014","relation":{"is-same-as":[{"id-type":"arxiv","id":"1408.5636","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.1408.5636","asserted-by":"subject"}]},"ISSN":["1860-5974"],"issn-type":[{"value":"1860-5974","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,9,10]]},"article-number":"1126"}}