BUILT-IN MATHEMATICA SYMBOL

BooleanCountingFunction

BooleanCountingFunction[k_max, n]
represents a Boolean function of n variables that gives True if at most variables are True.

BooleanCountingFunction[{k}, n]
represents a function of n variables that gives True if exactly k variables are True.

BooleanCountingFunction[{k_min, k_max}, n]
represents a function that gives True if between and variables are True.

BooleanCountingFunction[{{k₁, k₂, ...}}, n]
represents a function that gives True if exactly variables are True.

BooleanCountingFunction[spec, {a₁, a₂, ...}]
gives the Boolean expression in variables corresponding to the Boolean counting function specified by spec.

BooleanCountingFunction[spec, {a₁, a₂, ...}, form]
gives the Boolean expression in the form specified by form.

Details Details

BooleanCountingFunction[spec] gives a Boolean function object that works like Function.
BooleanCountingFunction[spec][a₁, a₂, ...] gives an implicit representation equivalent to the explicit Boolean expression BooleanCountingFunction[spec, {a₁, a₂, ...}].
BooleanConvert converts BooleanCountingFunction[spec][vars] to an explicit Boolean expression.
BooleanCountingFunction[{k_min, k_max, s}, ...] represents a function that gives True if , , ..., variables are True.
Any symmetric Boolean function can be represented uniquely using BooleanCountingFunction.
In BooleanCountingFunction[spec, {a₁, a₂, ...}, form], the possible forms are as given for BooleanConvert.
BooleanCountingFunction[spec, {a₁, a₂, ...}] by default gives an expression in disjunctive normal form (DNF).