BUILT-IN MATHEMATICA SYMBOL

# BooleanMinimize

BooleanMinimize[expr]
finds a minimal-length disjunctive normal form representation of expr.

BooleanMinimize[expr, form]
finds a minimal-length representation for expr in the specified form.

BooleanMinimize[expr, form, cond]
finds a minimal-length expression in the specified form that is equivalent to expr when cond is true.

## Details and OptionsDetails and Options

• BooleanMinimize[expr, form] always produces an expression equivalent to expr.
• Available forms are:
•  "DNF","SOP" disjunctive normal form, sum of products "CNF","POS" conjunctive normal form, product of sums "ANF" algebraic normal form "NOR" two-level Nor and Not "NAND" two-level Nand and Not "AND" two-level And and Not "OR" two-level Or and Not
• In general, there may be several minimal-length representations for a particular expression in a certain form. BooleanMinimize gives one of them.
• BooleanMinimize supports a Method option that specifies the detailed method to use.

## ExamplesExamplesopen allclose all

### Basic Examples (2)Basic Examples (2)

Find the minimal disjunctive normal form:

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A Boolean counting function in disjunctive normal form:

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Find a minimal disjunctive normal form:

 Out[2]=