{"@context":"https:\/\/schema.org\/","@type":"ScholarlyArticle","@id":"#article7832","name":"Circuits with Medium Fan-In","abstract":"We consider boolean circuits in which every gate may compute an arbitrary boolean function of k other gates, for a parameter k. We give an explicit function $f:{0,1}^n -> {0,1} that requires at least Omega(log^2(n)) non-input gates when k = 2n\/3. When the circuit is restricted to being layered and depth 2, we prove a lower bound of n^(Omega(1)) on the number of non-input gates. When the circuit is a formula with gates of fan-in k, we give a lower bound Omega(n^2\/k*log(n)) on the total number of gates. \r\n\r\nOur model is connected to some well known approaches to proving lower bounds in complexity theory. Optimal lower bounds for the Number-On-Forehead model in communication complexity, or for bounded depth circuits in AC_0, or extractors for varieties over small fields would imply strong lower bounds in our model. On the other hand, new lower bounds for our model would prove new time-space tradeoffs for branching programs and impossibility results for (fan-in 2) circuits with linear size and logarithmic depth. In particular, our lower bound gives a different proof for a known time-space tradeoff for oblivious branching programs.","keywords":["Boolean circuit","Complexity","Communication Complexity"],"author":[{"@type":"Person","name":"Hrubes, Pavel","givenName":"Pavel","familyName":"Hrubes"},{"@type":"Person","name":"Rao, Anup","givenName":"Anup","familyName":"Rao"}],"position":19,"pageStart":381,"pageEnd":391,"dateCreated":"2015-06-06","datePublished":"2015-06-06","isAccessibleForFree":true,"license":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/legalcode","copyrightHolder":[{"@type":"Person","name":"Hrubes, Pavel","givenName":"Pavel","familyName":"Hrubes"},{"@type":"Person","name":"Rao, Anup","givenName":"Anup","familyName":"Rao"}],"copyrightYear":"2015","accessMode":"textual","accessModeSufficient":"textual","creativeWorkStatus":"Published","inLanguage":"en-US","sameAs":"https:\/\/doi.org\/10.4230\/LIPIcs.CCC.2015.381","publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","isPartOf":{"@type":"PublicationVolume","@id":"#volume6236","volumeNumber":33,"name":"30th Conference on Computational Complexity (CCC 2015)","dateCreated":"2015-06-06","datePublished":"2015-06-06","editor":{"@type":"Person","name":"Zuckerman, David","givenName":"David","familyName":"Zuckerman"},"isAccessibleForFree":true,"publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","hasPart":"#article7832","isPartOf":{"@type":"Periodical","@id":"#series116","name":"Leibniz International Proceedings in Informatics","issn":"1868-8969","isAccessibleForFree":true,"publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","hasPart":"#volume6236"}}}