Simplify a Boolean Algebra expression with don't cares

I want to simplify this expression:

BooleanMinimize[(A ∧ ¬ B ∧ C ∧ ¬ D) ∨ (A ∧ B ∧ ¬ C ∧ ¬ D) ∨ (A ∧ B ∧ C ∧ ¬ D)]

And I get this:

(A ∧ B ∧ ¬ D) ∨ (A ∧ C ∧ ¬ D)

But using a Karnaugh Map and "don't cares" I get ¬ D. Is there anyway that I can get similar answer in Mathematica?

Answer

An arbitrary function with "don't cares" can be defined using either BooleanFunction or BooleanConvert, but in those cases, Mathematica makes no effort to find the minimal representation of such a function.

Instead, use BooleanMinimize with the optional third argument: an assumed condition on the variables. In your case, you can specify that your "don't cares" are 0-9 by making the condition be A ∧ (B ∨ C).

Then the calculation

BooleanMinimize[
  (A ∧ ¬ B ∧ C ∧ ¬ D) ∨ (A ∧ B ∧ ¬ C ∧ ¬ D) ∨ (A ∧ B ∧ C ∧ ¬ D),
  "DNF", 
  A ∧ (B ∨ C)]

will produce the desired output of !D.

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