Studies of Boolean functions/terminology
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 (Boolean) function, BF usually meant as BF with infinite arity and periodic truth table similar to Boolean expression
 truth table, TT usually meant as a truth table of finite length, determined by an arity
 valency ≤ adicity ≤ arity
 Valency is the number of arguments actually used. It is the number of circles in the Euler diagram.
 Adicity follows from the biggest atom. 2^{adicity} is the required TT length, or the period length of the infinite truth table.
 The term arity is used in two slightly different ways:
 arity n as an argument (e.g. of a class method) to get a finite truth table of length E.g. can be shown as 3ary
0000 0011
or as 4ary0000 0011 0000 0011
.  arity n as a shorthand for (as in: the 16 2ary Boolean functions)
 (For a while there may also be a third way, namely the erroneous use instead of valency or adicity.)
 arity n as an argument (e.g. of a class method) to get a finite truth table of length E.g. can be shown as 3ary
 atom Atoms are also called sets or arguments of a BF. what is usually shown by a circle and labeled A, B, C...
 atomvals the vector of atoms of a BF
 root A root BF has no gaps before or between the atoms. Its valency and adicity are equal. often called nondegenerate (The term dense might be more intuitive.)
root and atomvals 

A Boolean function is determined by its root and its atomvals.

 spread not root
 segment geometric element of an Euler diagram, e.g. its cells and the walls between them The number of segments in a Venn diagram is 3^{valency}.
dimension of a segment  

A segment has a dimension, namely the number of zeros in its ternary label. The relationships between segments that differ in only one digit are important:

 spot cell of an Euler diagram defined as segment with dimension 0 The number of spots in a Venn diagram is 2^{valency}.
 fullspot corresponds to true place in TT
 gapspot corresponds to false place in TT, but necessary for geometrically sound Euler diagram
 link connection between neighboring spots, i.e. wall between cells defined as segment with dimension 1
 border set of links that belong to the same atom, i.e. all walls of the same color
 split set without the notion of inside and outside usually the same as a partition into two blocks
 hypersplit generalization of a split partitions space into 2^{n} orthants
 filtrate reduction of a BF to a subset of its atoms, i.e. what remains when some circles are removed from the Euler diagram
 bundle part of an Euler diagram that is connected by crossing borders see e.g. decompose, multibundle 3221, 4ary bundles
 blighted arity can be reduced bloated or blotted (blight, blightless)
 bloated some arguments are equal or complementary to each other (bloat, bloatless)
 blotted some arguments are equal or complementary to niverse or empty set (blot, blotless)
 transformation signed permutation that turns elements of the same clan into each other
 clan negation and permutation equivalence class partitioned into families and factions
 family negation equivalence class
 faction permutation equivalence class
 cluster A cluster contains four or eight factions, that are complements and twins. (category)
 (Zhegalkin) twin Zhegalkin index interpreted as TT of the same length (E.g. all bits true and only left bit true are always twins, because the Zhegalkin index of the tautology is 1.)
 Zhegalkin index, Ж nonnegative integer identifying a Boolean function related to algebraic normal form
 representative some Boolean function that represents its whole equivalence class typically the smallest Zhegalkin index of a clan
 junior (senior) Boolean functions of arity n−1 are junior to those of arity n (and those of arity n+1 are senior)
 junarity (senarity) arity − 1 (arity + 1)
 gentle set of TTs is gentle, iff identical to set of twins
 foible The foibles are seven properties, that correspond to the vertices of a Fano plane. Most important are odd and odious.
 evil/odious foible of a BF, equal to last digit of TT odiousness also called depravity BF is odious, iff Ж has odd weight
 reverse BF with reversed TT
general terms
[edit  edit source]These words are sometimes used in variable names.
 recto and verso inside and outside of a set (see also split)
 powers of two and factorial
paltry  plenty  plethora  galore 