Properties of Boolean functions

Studies of Boolean functions

Properties of
Boolean functions

hard | soft
binary | binary
integer | integer
permutation | permutation
Family is a hard property. The image shows a family with eight members. Twin is a soft property. E.g. the twin of the tautology is always the NOR of all arguments.

Properties of Boolean functions are maps that assign values to Boolean functions.

Soft properties are dependent on arity.
For them the domain is always just the set of  2 2 n {\displaystyle 2^{2^{n}}} Boolean functions with arity  n {\displaystyle n} .

Hard properties are rarer, and probably more useful.
For them the domain can be the infinite set of all Boolean functions. (Typically the codomain will also be infinite, unless the values are Boolean.)

Properties of 3-ary BF are illustrated here: Boolf prop/3-ary
E.g. Boolf prop/3-ary/quaestor, Boolf prop/3-ary/patron

Below is a list of links to the respective chapters.  They are created with {{boolf-prop}}.

| hard  | soft

|
|

* weight
* nonlinearity
* atoms
* root
* family, faction, clan
* super-family, super-faction, super-clan
* prefect
* legion, cohort

* ultra-family, ultra-clan
* tribe
* principality, dominion
* squad, platoon, company

binary  |

* linear
* seal, seal block
* balanced, light, heavy
* openness, closed, ajar, open, unclosed, unopen
* dense
* strong
* monotonic
* parity, odd, even
* depravity, odious, evil
* quadrant, ugly
* gender, male, female
* honesty, honest, dishonest

* sharp, blunt
* rude
* rough
* acute, obtuse
* noble
* symmetric

integer  |

* valency
* adicity
* arity
* strength
* gravity, depth

* soft weight
* soft nonlinearity
* soft gravity, soft depth
* consul, signed consul, consul weight
* patron
* praetor
* quaestor

permutation  |

* complement
* reverse
* dual

* half-complement
* twin
* partner, friend