Linearity of boolean expressions

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SUMMARY

This discussion centers on determining the linearity of multi-variable boolean expressions in Sum of Products (SOP) form. The participants explore whether expressions such as (x OR y) can be classified as linear and question the definition of linearity in this context. It is established that traditional algebraic linearity, which pertains to multiplication with respect to addition, does not directly apply to boolean algebra. The consensus is that a clear definition of "linear" in relation to SOP representations is lacking.

PREREQUISITES
  • Understanding of boolean algebra concepts
  • Familiarity with Sum of Products (SOP) representation
  • Knowledge of logical operators: AND, OR, NOT
  • Basic principles of algebraic linearity
NEXT STEPS
  • Research the definition of linearity in boolean algebra
  • Explore the implications of linearity on boolean functions
  • Study the properties of Sum of Products (SOP) and Product of Sums (POS) forms
  • Investigate applications of boolean expressions in digital circuit design
USEFUL FOR

Mathematicians, computer scientists, electrical engineers, and anyone involved in digital logic design or boolean algebra analysis.

m~ray
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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?
 
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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.
 
my funtions will have only OR, AND and NOT operators.. written in the SOP form.
 
How do you define "linear" in this context?
 
yes, this was my question. How do we define linearity when we are dealing with a sum of product representation of multivariable boolean expressions.
 
m~ray said:
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?
 

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