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BooleanCountingFunction

Represents the Boolean function of n variables that is True when the number of True arguments is one the specification names: k for at most k, {k} for exactly k, {kmin, kmax} for a range, and {{k1, k2, …}} for a set of counts.

Applied to Boolean arguments it answers directly:

$ wo 'BooleanCountingFunction[2, 4][True, True, False, False]'
True

$ wo 'BooleanCountingFunction[{2}, 3][True, False, False]'
False

$ wo 'BooleanCountingFunction[{{1, 3}}, 3][True, True, True]'
True

A count past the number of variables simply never matches:

$ wo 'BooleanCountingFunction[{4}, 3][True, True, True]'
False

Given a list of variables it writes out the expression instead, and a third argument names the form:

$ wo 'BooleanCountingFunction[{{2}}, {a, b, c}]'
(a && b &&  !c) || (a &&  !b && c) || ( !a && b && c)

$ wo 'BooleanCountingFunction[2, {a, b, c}, "CNF"]'
 !a ||  !b ||  !c

An invalid specification is reported:

$ wo 'BooleanCountingFunction[{-1}, 2]'

BooleanCountingFunction::bspec: BooleanCountingFunction[{-1}, 2] is not a valid BooleanCountingFunction specification.
BooleanCountingFunction[{-1}, 2]