{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:50Z","timestamp":1753893830675,"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>We study the asymptotic relation between the probability and the complexity of Boolean functions\u00a0in the implicational fragment which are generated by large random Boolean expressions involving\u00a0variables and implication, as the number of variables tends to infinity. In contrast to models\u00a0studied in the literature so far, we consider two expressions to be equal if they differ only in\u00a0the order of the premises. A precise asymptotic formula is derived for functions of low\u00a0complexity. Furthermore, we show that this model does not exhibit the Shannon effect.An erratum was added to this paper on Feb 20, 2014.<\/jats:p>","DOI":"10.37236\/2402","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T03:27:34Z","timestamp":1578713254000},"source":"Crossref","is-referenced-by-count":4,"title":["Probabilities of Boolean Functions given by Random Implicational Formulas"],"prefix":"10.37236","volume":"19","author":[{"given":"Antoine","family":"Genitrini","sequence":"first","affiliation":[]},{"given":"Bernhard","family":"Gittenberger","sequence":"additional","affiliation":[]},{"given":"Veronika","family":"Kraus","sequence":"additional","affiliation":[]},{"given":"C\u00e9cile","family":"Mailler","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2012,6,6]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v19i2p37\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v19i2p37\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T22:33:51Z","timestamp":1579300431000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v19i2p37"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,6,6]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2012,4,7]]}},"URL":"https:\/\/doi.org\/10.37236\/2402","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2012,6,6]]},"article-number":"P37"}}