{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:06Z","timestamp":1753893786328,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>The Ehrenfeucht-Fraisse game is a two-person game of perfect information which is connected to the Zero-One Laws of first order logic.  We give bounds for roughly how quickly the Zero-One Laws converge for random bit strings and random circular bit sequences. We measure the tenaciousness of the second player (\"Duplicator\") in playing the Ehrenfeucht-Fraisse game, by bounding the numbers of moves Duplicator can play and win with probability $1-\\epsilon$. We show that for random bit strings and random circular sequences of length $n$ generated with a low probability ($p\\ll n^{-1}$), the number of moves, $T_{\\epsilon}(n)$, is $\\Theta(\\log_2 n)$. For random bit strings and circular sequences with isolated ones ($n^{-1}\\ll p \\ll n^{-1\/2}$), $T_{\\epsilon}(n) = O(\\min(\\log_2 np, -\\log_2 np^2))$.  For $n^{-1\/2}\\ll p$ and $(1-p) \\ll n^{-1\/2}$, we show that $T_{\\epsilon}(n) = O(\\log^* n)$ for random circular sequences, where $\\log^* n$ has the usual definition\u2013 the least number of times you iteratively apply the logarithm to get a value less than one.<\/jats:p>","DOI":"10.37236\/1616","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T02:17:25Z","timestamp":1578709045000},"source":"Crossref","is-referenced-by-count":2,"title":["The Tenacity of Zero-One Laws"],"prefix":"10.37236","volume":"8","author":[{"given":"Joel H.","family":"Spencer","sequence":"first","affiliation":[]},{"given":"Katherine","family":"St. John","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2000,8,6]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v8i2r17\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v8i2r17\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T05:22:26Z","timestamp":1579324946000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v8i2r17"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2000,8,6]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2001,2,6]]}},"URL":"https:\/\/doi.org\/10.37236\/1616","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2000,8,6]]},"article-number":"R17"}}