Talk:Balanced Boolean function: Difference between revisions

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Revision as of 17:32, 5 September 2010 edit Abdull (talk \| contribs) Extended confirmed users, Pending changes reviewers 6,856 edits Wrong examples?		Latest revision as of 19:23, 5 August 2024 edit undo David Eppstein (talk \| contribs) Autopatrolled, Administrators 235,633 edits start-class
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Line 1: {{WikiProject banner shell\|class=Start\|1= {{WikiProject Computer science}} {{WikiProject Mathematics\|importance=low}} }} == Wrong examples? == Line 6 ⟶ 11: *Regarding the second example: 0 is usually understood as being neither positive nor negative. Therefore there will be one more element in the set that is assigned ''0'' compared to the set that is assigned ''1''. Is it correct to still speak of this function being ''balanced''? --[[User:Abdull\|Abdull]] ([[User talk:Abdull\|talk]]) 17:32, 5 September 2010 (UTC) This page was copied from the abstract of the article cited! It needs to be deleted or re-written. <span style="font-size: smaller;" class="autosigned">— Preceding [[Wikipedia:Signatures\|unsigned]] comment added by [[Special:Contributions/131.122.6.28\|131.122.6.28]] ([[User talk:131.122.6.28\|talk]]) 12:21, 20 March 2012 (UTC)</span><!-- Template:Unsigned IP --> <!--Autosigned by SineBot--> In my opinion, this article is very weak. I have never edited wikipedia but I have two suggestions. These should make the article more useful for researchers. 1. Mention some elementary properties of balanced boolean functions. Example 1: a balanced boolean function of dimension D+1 can be created by concatenating any dimension D boolean function with its complement. Example 2: balanced boolean functions have the unique property that their complement is also balanced. Example 3: The randomization lemma (See the famous coding theory book by Sloane and MacWilliams) 2. Mention the Cusick-Cheon conjecture. The Cusick-Cheon conjecture deals with a fundamental characterization of balanced boolean functions in terms of the degree of their algebraic normal form representation. It is very likely that the Cusick-Cheon conjecture is true because it is backed by good numerical evidence although it has only been proven in special cases. <!-- Template:Unsigned IP --><small class="autosigned">— Preceding [[Wikipedia:Signatures\|unsigned]] comment added by [[Special:Contributions/24.179.214.114\|24.179.214.114]] ([[User talk:24.179.214.114#top\|talk]]) 21:54, 31 May 2019 (UTC)</small> <!--Autosigned by SineBot-->