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Legacy Documentation

Mathematica 8 (2010)

This is documentation for Mathematica 8, which was
based on an earlier version of Wolfram Language.
View current documentation (Version 14.3)

BooleanMinimize

BooleanMinimize [expr]
finds a minimal-length disjunctive normal form representation of expr.
BooleanMinimize
finds a minimal-length representation for expr in the specified form.
BooleanMinimize
finds a minimal-length expression in the specified form that is equivalent to expr when cond is true.
  • 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.
(2)
Find the minimal disjunctive normal form:
A Boolean counting function in disjunctive normal form:
Find a minimal disjunctive normal form:
Find the minimal disjunctive normal form:
Out[1]=
A Boolean counting function in disjunctive normal form:
Out[1]=
Find a minimal disjunctive normal form:
Out[2]=
(2)
A Boolean function of five variables represented in DNF:
Minimal-length DNF:
Minimal-length CNF:
Minimal-length NAND form:
Minimal-length NOR form:
Minimal-length ANF:
Show that all the forms are equivalent:
Minimize a Boolean function using a "care set" or condition:
The resulting forms are equivalent when cond is true:
They are not equivalent without the condition:
Typically the forms are longer without conditions:
(1)
Compute the minimal DNF representation:
Plot the size as a function of index:
Get its distribution:
Compute the size for the first 1000 four-variable functions:
(4)
The output from BooleanMinimize is equivalent to its input:
The output from BooleanMinimize with condition is conditionally equivalent to its input:
The forms f and g are equivalent when cond is true:
They are not equivalent on their own:
The minimal lengths "DNF", "CNF", "NAND", or "NOR" are not unique:
BooleanMinimize will produce an expression of length 3:
Another equivalent expression of length 3 is given by exchanging b and c:
Similar examples for "CNF", "NAND", and "NOR":
Use BooleanConvert when the minimal length form is not required:
BooleanConvert can also convert to additional forms:
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