finds a minimal-length disjunctive normal form representation of expr.
finds a minimal-length representation for expr in the specified form.
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.
Examplesopen allclose all
Basic Examples (2)
A Boolean function of five variables represented in DNF:
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:
Properties & Relations (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:
Wolfram Research (2008), BooleanMinimize, Wolfram Language function, https://reference.wolfram.com/language/ref/BooleanMinimize.html.
Wolfram Language. 2008. "BooleanMinimize." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/BooleanMinimize.html.
Wolfram Language. (2008). BooleanMinimize. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/BooleanMinimize.html