Linearity of boolean expressions

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Discussion Overview

The discussion revolves around the concept of linearity in the context of sum of products (SOP) representations of multivariable boolean expressions. Participants explore how to determine if a boolean expression is linear, particularly when involving OR, AND, and NOT operators.

Discussion Character

  • Conceptual clarification, Debate/contested

Main Points Raised

  • One participant asks how to judge if a given SOP form of a boolean expression is linear, specifically questioning if expressions like (x or y) can be considered linear.
  • Another participant notes that algebraic linearity pertains to multiplication with respect to addition and prompts for clarification on what operations are being tested for linearity.
  • A participant specifies that their functions will only include OR, AND, and NOT operators in SOP form.
  • There is a request for a definition of "linear" in this specific context, indicating a need for clarity on the term's application to boolean expressions.
  • One participant reiterates the question about defining linearity in the context of SOP representations and expresses uncertainty about whether "linear" is a defined term in this scenario.

Areas of Agreement / Disagreement

Participants express uncertainty about the definition of linearity in the context of boolean expressions, indicating that there is no consensus on how to approach the concept.

Contextual Notes

There is a lack of clarity regarding the definition of linearity when applied to boolean expressions, and the discussion does not resolve this ambiguity.

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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