# 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 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.

# Examples

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## 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:

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