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I have been trying to understand the polytope model used for loop nest optimizations. Now while going through some of the thesis written on this, i came across the term/phrase "linear code" a number of times in relation to whether a particular loop can be executed in parallel. The following is a text from one of the thesis:

The theory concerning loop analyses and transformations is unified in a well known mathematical framework called the polytope model. However, it's applicability is limited to array-based scientific applications exhibiting explicit linearity.

As far as my knowledge (which is limited) is concerned, i think it has to do something with the memory accesses and loop bounds . I am not from a CS background and hence don't have much theoretical knowledge, if this is a topic taught in a typical CS class. If not i would like to know what is it, i am just not able to get a hang of it.

If anyone can provide a detailed explanation that would be good or any resources where i can learn about this, that would also do great.

P.S : I am happy to make any further editions or add details which may be require to answer it better.

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    $\begingroup$ Could you provide more context? The text you quote doesn't include the term "linear code". $\endgroup$ – David Richerby Apr 21 '16 at 15:26
  • $\begingroup$ @DavidRicherby, I think OP means this paper: arxiv.org/pdf/0805.1301v2.pdf $\endgroup$ – Johan May 5 '16 at 18:09

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