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From: "Dmitry A. Kazakov" <mailbox@dmitry-kazakov.de>
Subject: Re: Test tool not only for Ada
Newsgroups: comp.lang.ada
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Date: Fri, 25 Jan 2008 10:31:04 +0100
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Date: 2008-01-25T10:31:05+01:00
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On Fri, 25 Jan 2008 08:48:35 -0000, Stuart wrote:

> The interesting challenge for 'Abstract Interpretation' tools is deciding 
> how much detail to preserve at each stage.  From the example should the tool 
> note that 'y' might have the values 2..40 or the set of values {2, 4, 6, 
> ..., 40}.
> 
> This can become important, for instance if you had the statement:
>    z := 1000 / (y - 9);
> 
> Could a divide by zero occur?  If you had a lax model of 'y'  [2..40] you 
> would be concerned, but a more accurate model would dispel the concern.

There is another difficult aspect of the problem of uncertain computations.
It is dependency analysis. For example:

   y := x;
   z := x * y;

When x is in [-1, 2] then without knowing that y equals x, i.e. assuming
that x and y are independent, the best possible estimation of z is [-2, 4].
With this knowledge it is [0, 4].

-- 
Regards,
Dmitry A. Kazakov
http://www.dmitry-kazakov.de