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- Noble Boolean functions are those who are their own [[Zhegalkin twins]], i.e. the binary expression When a Boolean function is noble, its whole [[Boolf-EC#P|faction]] is noble.<br> ...9 KB (1,361 words) - 11:15, 18 May 2024
- The mentor is a rather dubious [[Soft properties of Boolean functions|soft property]] of a BF. But it seems surprisingly interesting.<br> ...a [[Boolf-hard#family|family matrix]], getting the senior [[Noble Boolean functions|nobles]] of its rows, and getting their [[Boolf-hard#prefect|prefects]].<br ...8 KB (1,123 words) - 19:14, 10 January 2025
- {{Properties of Boolean functions/header}} [[File:Boolean functions like 0110 1000.svg|thumb|[[Boolf-hard#family|''Family'']] is a hard propert ...3 KB (366 words) - 12:58, 15 March 2025
- Boolean functions belong to the same family, when they can be [[Studies of Euler diagrams/tra Each row (or column) is the truth table of a Boolean functions in the family. ...6 KB (980 words) - 01:21, 16 March 2025
- ...arity}} of a Boolean function measures how far it is from being a [[linear Boolean function]].<br> As an integer it is a [[Soft properties of Boolean functions|soft property]] <small>(i.e. dependent on arity)</small>. ...4 KB (568 words) - 21:50, 17 February 2025
- [[File:Venn 0101 0011.svg|thumb|The 3-ary Boolean function <math>\scriptstyle ( A \land \neg C ) \lor ( B \land C )</math> re [[File:Boolean functions like 1100 1010.svg|thumb|''sec'' 53 containing 8 functions, including the one shown above (shown in the top right position)]] ...80 KB (10,872 words) - 11:16, 17 May 2024
- Analogous to hard and soft [[properties of Boolean functions]], there are also hard and soft permutations. ...mutation is '''hard''', when the domain is the infinite set of all Boolean functions.<br> ...2 KB (240 words) - 12:46, 14 March 2025
- ...0000 0001 0001 0110.png|thumb|280px|[[w:Venn diagram|Venn diagram]] of the Boolean function<br>0000 0001 0001 0110]] There are <math>2^{2^{4}}</math> = 65536 4-ary Boolean functions, which correspond to 16-bit binary strings. ...104 KB (7,501 words) - 11:49, 12 January 2025
- {{Properties of Boolean functions/header}} ...ions|Nonlinearity]]''' is the extent to which a BF is not [[Linear Boolean functions|linear]]. <small>It is usually shown as an integer for a given arity ({{boo ...4 KB (593 words) - 00:53, 15 March 2025
- {{Properties of Boolean functions/header}} |colspan="2"| [[File:3-ary Boolean functions; super-family of Zhe 40.svg|200px]] ...3 KB (404 words) - 17:01, 14 March 2025
- ...en arity, the [[Linear Boolean functions|linears]] and the [[Noble Boolean functions|nobles]] are important subsets. Each linear can be assigned a [[Noble Boolean functions#patrons|patron]], which is noble. Each noble can be assigned a prefect, whi ...10 KB (1,373 words) - 01:14, 20 December 2024
- ...all>The integers describe the truth tables. Compare [[c:File:3-ary Boolean functions; faction cluster 4x6 (1); graph.svg|this]] file, which is also shown [[#3-a It is possible two extend the twin relationship to sets of Boolean functions. Two sets <math>A, B</math> are twins, iff <math>a \in A \implies \operator ...8 KB (896 words) - 23:27, 16 May 2024
- ...infinite arity and periodic truth table {{spaces|4}} <small>similar to {{w|Boolean expression}}</small> ...or <math>adicity \le n</math> <small>(as in: ''the 16 2-ary Boolean functions'')</small> ...13 KB (1,832 words) - 14:00, 11 March 2025
- See also [[Integer sequences related to Boolean functions/clans|.../clans]]. Which Boolean function an integer represents, depends on the arity. ...4 KB (501 words) - 18:53, 4 March 2025
- {{Properties of Boolean functions/header}} ...rthand for adicity ≤ ''n'' <small>(as in: ''the 16 2-ary Boolean functions'')</small> ...2 KB (294 words) - 17:03, 14 March 2025
Page text matches
- ...n arbitrary set and where <math>\mathbb{B}</math> is a [[../BooleanDomain/|boolean domain]]. ...olean function''' (of finite [[../Bijective/|arity]] <math>k</math>) is a boolean-valued function of type <math>f : \mathbb{B}^k \to \mathbb{B}</math>. ...886 bytes (129 words) - 03:59, 1 July 2015
- {{Properties of Boolean functions/header}} [[File:Boolean functions like 0110 1000.svg|thumb|[[Boolf-hard#family|''Family'']] is a hard propert ...3 KB (366 words) - 12:58, 15 March 2025
- Analogous to hard and soft [[properties of Boolean functions]], there are also hard and soft permutations. ...mutation is '''hard''', when the domain is the infinite set of all Boolean functions.<br> ...2 KB (240 words) - 12:46, 14 March 2025
- {{Properties of Boolean functions/header}} |colspan="2"| [[File:3-ary Boolean functions; super-family of Zhe 40.svg|200px]] ...3 KB (404 words) - 17:01, 14 March 2025
- ...k \to \mathbb{B},</math> where <math>\mathbb{B} = \{ 0, 1 \}</math> is a [[boolean domain]] and where <math>k\!</math> is a nonnegative integer. In the case There are <math>2^{2^k}</math> such functions. These play a basic role in questions of [[complexity theory]] as well as ...5 KB (568 words) - 16:06, 8 September 2022
- ...ath>, in particular, to define all of the finitary [[../Predicate/|boolean functions]], <math>f : \mathbb{B}^k \to \mathbb{B}</math>. ...748 bytes (106 words) - 05:01, 1 July 2015
- {{Properties of Boolean functions/header}} ...rthand for adicity ≤ ''n'' <small>(as in: ''the 16 2-ary Boolean functions'')</small> ...2 KB (294 words) - 17:03, 14 March 2025
- See also [[Integer sequences related to Boolean functions/clans|.../clans]]. Which Boolean function an integer represents, depends on the arity. ...4 KB (501 words) - 18:53, 4 March 2025
- ...gebraic normal form}}''' ('''ANF''') is a {{w|canonical normal form}} of a Boolean function. The ANF allows to assign every Boolean function (regardless of its arity) a unique integer, which shall be called ...3 KB (509 words) - 23:24, 16 May 2024
- {{Properties of Boolean functions/header}} ...ions|Nonlinearity]]''' is the extent to which a BF is not [[Linear Boolean functions|linear]]. <small>It is usually shown as an integer for a given arity ({{boo ...4 KB (593 words) - 00:53, 15 March 2025
- Boolean functions belong to the same family, when they can be [[Studies of Euler diagrams/tra Each row (or column) is the truth table of a Boolean functions in the family. ...6 KB (980 words) - 01:21, 16 March 2025
- ...eis|A195467}}) and to the '''[[algebraic normal form]]''' (ANF) of Boolean functions.<br> ...functions. The column index is the '''Zhegalkin index''' of the respective Boolean function. ...5 KB (662 words) - 00:12, 25 January 2025
- ...arity}} of a Boolean function measures how far it is from being a [[linear Boolean function]].<br> As an integer it is a [[Soft properties of Boolean functions|soft property]] <small>(i.e. dependent on arity)</small>. ...4 KB (568 words) - 21:50, 17 February 2025
- ...olflink|dukeli}} contains <math>\frac{16 \cdot 24}{2} = 192</math> Boolean functions.<br> ...each function, which makes it a complete [[Equivalence classes of Boolean functions#NPN|NPN equivalence class]].</small> ...5 KB (610 words) - 18:29, 11 February 2023
- The mentor is a rather dubious [[Soft properties of Boolean functions|soft property]] of a BF. But it seems surprisingly interesting.<br> ...a [[Boolf-hard#family|family matrix]], getting the senior [[Noble Boolean functions|nobles]] of its rows, and getting their [[Boolf-hard#prefect|prefects]].<br ...8 KB (1,123 words) - 19:14, 10 January 2025
- Noble Boolean functions are those who are their own [[Zhegalkin twins]], i.e. the binary expression When a Boolean function is noble, its whole [[Boolf-EC#P|faction]] is noble.<br> ...9 KB (1,361 words) - 11:15, 18 May 2024
- *Applying principles of Boolean Algebra to minimize given function =Boolean Algebra= ...4 KB (594 words) - 09:09, 8 July 2023
- These images represent the 4-ary Boolean function <math>(\neg C \and \neg D) \or (\neg A \and B \and \neg D) \or (\n and is part of [[commons:File:4-ary Boolean functions in BEC 127 from 1100 1010 1000 1000.svg#File|BEC 127]] <small>(rows (22,2) ...5 KB (803 words) - 22:51, 26 June 2022
- ...all>The integers describe the truth tables. Compare [[c:File:3-ary Boolean functions; faction cluster 4x6 (1); graph.svg|this]] file, which is also shown [[#3-a It is possible two extend the twin relationship to sets of Boolean functions. Two sets <math>A, B</math> are twins, iff <math>a \in A \implies \operator ...8 KB (896 words) - 23:27, 16 May 2024
- ==Walsh spectrum of Boolean functions== The Walsh spectrum of a Boolean function is the product of it's binary string representation and a [[w:Wals ...6 KB (843 words) - 18:40, 15 January 2018