# Linearity of boolean expressions

m~ray
given an sop form of a multi variable boolean expression, how to judge if it is linear or not?
is (x or y) linear?
more generally, can a function be linear with an and in sop form?

## Answers and Replies

Science Advisor
Gold Member
Algebraic linearity is for multiplication wrt addition.

What operations are you testing for linearity?

Once those are specified, and verified for linearity, then you can test your functions.

m~ray
my funtions will have only OR, AND and NOT operators.. written in the SOP form.

Science Advisor
How do you define "linear" in this context?

m~ray
yes, this was my question. How do we define linearity when we are dealing with a sum of product representation of multivariable boolean expressions.

Science Advisor
yes, this was my question. How do we define linearity when we are dealing with a sum of product representation of multivariable boolean expressions.
I don't know. As far as I know, "linear" is not defined in this context. But I don't know evereything. How did this question come up?