Wolfram Language & System 12.0 (2019)|Legacy Documentation

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BooleanFunction

BooleanFunction[k,n]

represents the k Boolean function in n variables.

BooleanFunction[values]

represents the Boolean function corresponding to the specified vector of truth values.

BooleanFunction[{{i₁₁,i₁₂,…}o₁,…}]

represents the Boolean function defined by the specified mapping from inputs to outputs.

BooleanFunction[spec,{a₁,a₂,…}]

gives the Boolean expression in variables a_i corresponding to the Boolean function specified by spec.

BooleanFunction[spec,{a₁,a₂,…},form]

gives the Boolean expression in the form specified by form.

Details

BooleanFunction[spec] gives a Boolean function object that works like Function.
BooleanFunction[spec][a₁,a₂,…] gives an implicit representation equivalent to the explicit Boolean expression BooleanFunction[spec,{a₁,a₂,…}].
BooleanConvert converts BooleanFunction[spec][vars] to an explicit Boolean expression.
In BooleanFunction[values] etc., values can be specified either as True and False or as 1 and 0.
The functions represented by BooleanFunction always return True or False.
In BooleanFunction[values], the values are specified in binary order starting with 111, ….
BooleanFunction[k,n] is equivalent to BooleanFunction[IntegerDigits[k,2,2^n]].
In BooleanFunction[values], each value can be a list, representing a vector-valued Boolean function.
In BooleanFunction[{{i₁₁,i₁₂,…}->o₁,…}] the o_i can be lists, representing vector-valued Boolean functions.
Elements of both inputs and outputs can be specified either as True and False or as 1 and 0.
Elements of inputs and outputs can also include any number of _, representing "don't cares".
They can also include up to one __, representing a sequence of "don't cares".
In BooleanFunction[spec,{a₁,a₂,…},form], the possible forms are as given for BooleanConvert.
BooleanFunction[spec,{a₁,a₂,…}] by default gives an expression in DNF.
BooleanFunction[k] gives the k Boolean function in n variables, where n has the smallest value for which .
The numbering of Boolean functions in BooleanFunction[k,…] is consistent with CellularAutomaton.
BooleanFunction[CellularAutomaton[n]] is equivalent to BooleanFunction[n,3].
BooleanFunction[CellularAutomaton[{n,2,r}]] is equivalent to BooleanFunction[n,2r+1].
Operations such as BooleanMinimize, BooleanTable, etc. can operate directly on BooleanFunction objects.
BooleanFunction objects can be applied to variables just like other Boolean functions such as And, Or, etc.
In StandardForm and related formats, BooleanFunction objects are printed in elided form, with only their number of variables displayed.
BooleanVariables gives the number of variables of a BooleanFunction object.