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• And-inverter graph, using only AND and NOT

In order to optimize electronic circuits, Boolean formulas can be minimized using the Quine–McCluskey algorithm or Karnaugh map.

A Boolean function can have a variety of properties:cite-ref-0-7-0[7]

• Constant: Is always true or always false regardless of its arguments.

• Monotone: for every combination of argument values, changing an argument from false to true can only cause the output to switch from false to true and not from true to false. A function is said to be unate in a certain variable if it is monotone with respect to changes in that variable.

• Linear: for each variable, flipping the value of the variable either always makes a difference in the truth value or never makes a difference (a parity function).

• Symmetric: the value does not depend on the order of its arguments.

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