Editing Boolean function (section)

===Properties===

A Boolean function can have a variety of properties:<ref name=":0">{{Cite web|title=Boolean functions — Sage 9.2 Reference Manual: Cryptography|url=https://doc.sagemath.org/html/en/reference/cryptography/sage/crypto/boolean_function.html|access-date=2021-05-01|website=doc.sagemath.org}}</ref>

* [[Constant function|Constant]]: Is always true or always false regardless of its arguments.
* [[Monotonic function#In Boolean functions|Monotone]]: for every combination of argument values, changing an argument from false to true can only cause the output to switch from false to true and not from true to false. A function is said to be [[Unate function|unate]] in a certain variable if it is monotone with respect to changes in that variable. 
* [[Linearity#Boolean functions|Linear]]: for each variable, flipping the value of the variable either always makes a difference in the truth value or never makes a difference (a [[parity function]]).
* [[Symmetric Boolean function|Symmetric]]: the value does not depend on the order of its arguments.
* [[Read-once function|Read-once]]: Can be expressed with [[logical conjunction|conjunction]], [[logical disjunction|disjunction]], and [[negation]] with a single instance of each variable.
*[[Balanced Boolean function|Balanced]]: if its [[truth table]] contains an equal number of zeros and ones. The [[Hamming weight]] of the function is the number of ones in the truth table.
* [[Bent function|Bent]]: its derivatives are all balanced (the autocorrelation spectrum is zero)
* [[Correlation immunity|Correlation immune]] to ''m''th order: if the output is uncorrelated with all (linear) combinations of at most ''m'' arguments
*[[Evasive Boolean function|Evasive]]: if evaluation of the function always requires the value of all arguments
*A Boolean function is a ''Sheffer function'' if it can be used to create (by composition) any arbitrary Boolean function (see [[functional completeness]])
*The ''algebraic degree'' of a function is the order of the highest order monomial in its [[algebraic normal form]]
[[Circuit complexity]] attempts to classify Boolean functions with respect to the size or depth of circuits that can compute them.