{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,28]],"date-time":"2026-01-28T18:43:15Z","timestamp":1769625795690,"version":"3.49.0"},"reference-count":39,"publisher":"Association for Computing Machinery (ACM)","issue":"5","license":[{"start":{"date-parts":[[2017,11,15]],"date-time":"2017-11-15T00:00:00Z","timestamp":1510704000000},"content-version":"vor","delay-in-days":365,"URL":"http:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"funder":[{"DOI":"10.13039\/501100003977","name":"Israel Science Foundation","doi-asserted-by":"crossref","award":["1402\/14"],"award-info":[{"award-number":["1402\/14"]}],"id":[{"id":"10.13039\/501100003977","id-type":"DOI","asserted-by":"crossref"}]},{"name":"Weizmann Institute of Science National Postdoctoral Award Program for Advancing Women in Science"},{"name":"I-CORE Program of the Planning and Budgeting Committee"},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["CCF-1412958"],"award-info":[{"award-number":["CCF-1412958"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["J. ACM"],"published-print":{"date-parts":[[2016,12,20]]},"abstract":"<jats:p>\n                    We show an exponential gap between communication complexity and information complexity by giving an explicit example of a partial boolean function with information complexity \u2264\n                    <jats:italic toggle=\"yes\">O<\/jats:italic>\n                    (\n                    <jats:italic toggle=\"yes\">k<\/jats:italic>\n                    ), and distributional communication complexity \u2265 2\n                    <jats:sup>\n                      <jats:italic toggle=\"yes\">k<\/jats:italic>\n                    <\/jats:sup>\n                    . This shows that a communication protocol cannot always be compressed to its internal information. By a result of Braverman [2015], our gap is the largest possible. By a result of Braverman and Rao [2014], our example shows a gap between communication complexity and amortized communication complexity, implying that a tight direct sum result for distributional communication complexity cannot hold, answering a long-standing open problem.\n                  <\/jats:p>\n                  <jats:p>\n                    Another (conceptual) contribution of our work is the\n                    <jats:italic toggle=\"yes\">relative discrepancy<\/jats:italic>\n                    method, a new rectangle-based method for proving communication complexity lower bounds for boolean functions, powerful enough to separate information complexity and communication complexity.\n                  <\/jats:p>","DOI":"10.1145\/2907939","type":"journal-article","created":{"date-parts":[[2016,11,17]],"date-time":"2016-11-17T11:33:35Z","timestamp":1479382415000},"page":"1-31","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":15,"title":["Exponential Separation of Information and Communication for Boolean Functions"],"prefix":"10.1145","volume":"63","author":[{"given":"Anat","family":"Ganor","sequence":"first","affiliation":[{"name":"Weizmann Institute of Science, Rehovot, Israel"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Gillat","family":"Kol","sequence":"additional","affiliation":[{"name":"Institute for Advanced Study"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ran","family":"Raz","sequence":"additional","affiliation":[{"name":"Weizmann Institute of Science and the Institute for Advanced Study"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2016,11,15]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcss.2003.11.006"},{"key":"e_1_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.1137\/100811969"},{"key":"e_1_2_1_3_1","unstructured":"Balthazar Bauer Shay Moran and Amir Yehudayoff. 2015. 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