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From: Peter Bishop < >

Date: Tue, 10 Mar 2015 09:50:10 +0000

Now I think I understand your point.

You just object to the term *software* reliability*
Received on Tue Mar 10 2015 - 10:50:33 CET
*

Date: Tue, 10 Mar 2015 09:50:10 +0000

Now I think I understand your point.

You just object to the term *software* reliability

If the term was *system* reliability in an specified operational environment, and the system contained software and the failure was always caused by software - I take it that would be OK?

A alternative term like *software integrity* or some such would be needed to describe the property of being correct or wrong on a given input. (In a lot of mathematical models this is represented as a "score function" that is either true or false for each possible input)

Peter Bishop

Nick Tudor wrote:

*> Now back in the office...for a short while.*

*> *

*> Good point David - well put. *

*> *

*> I would have responded: There exists a person N who knows a bit about *

*> mathematics. Person N applies some mathematics and asserts Truth. *

*> Unfortunately, because of the incorrect application of the mathematics, *

*> the claims N now makes cannot be relied upon. The maths might well be *

*> correct, but the application is wrong because - and I have to say it yet *

*> again - the application misses fails to acknowledge that it is the *

*> environment that is random rather than the software. Software *

*> essentially boils down to a string of one's and nought's. Given the same *

*> inputs (and that always comes from the chaotic environment) then the *

*> output will always be the same. It therefore makes no sense to talk *

*> about 'software reliability'.*

*> *

*> Nick Tudor*

*> Tudor Associates Ltd*

*> Mobile: +44(0)7412 074654*

*> www.tudorassoc.com <http://www.tudorassoc.com>*

*> **

*> **

*> *77 Barnards Green Road**

*> *Malvern**

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*> Company No. 07642673**

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*> *

*> On 9 March 2015 at 12:26, David Haworth <david.haworth_at_xxxxxx
> <mailto:david.haworth_at_xxxxxx
> *

> Peter,

>

> there's nothing wrong with the mathematics, but I've got

> one little nit-pick about its application in the real world.

>

> The mathematics you describe gives two functions f and g,

> one of which is the model, the other is the implementation.

>

> In practice, your implementation runs on a computer and so the

> domain and range are not "the continuum". If your model is mathematical

> (or even runs on a different computer), the output of one will

> necessarily be different from the output of the other. That

> may not be a problem in the discrete sense - you simply specify a

> tolerance t > 0 in the form of:

>

> Corr-f-g(i) = 0 if and only if |f(i)-g(i)| < t

>

> etc.

>

> The problem becomes much larger in the real world of control

> systems where the output influences the next input of the

> sequence. The implementation and the model will tend to drift

> apart. In the worst case what might be nice and stable in the

> model might exhibit unstable behaviour in the implementation.

>

> You're then in the subject of mathematical chaos, where a

> perfectly deterministic system exhibits unstable and unpredictable

> behaviour. However, this email is too small to describe it. :-)

>

> Cheers,

> Dave

>

> On 2015-03-09 11:48:57 +0100, Peter Bernard Ladkin wrote:

> > Nick,

> >

> > Consider a mathematical function, f with domain D and range R.

> Given input i \in D, the output is f(i).

> >

> > Consider another function, g, let us say for simplicity with the

> same input domain D and range R.

> >

> > Define a Boolean function on D, Corr-f-g(i):

> >

> > Corr-f-g(i) = 0 if and only if f(i)=g(i);

> > Corr-f-g(i) = 1 if and only if f(i) NOT-EQUAL g(i)

> >

> > If X is a random variable taking values in D, then f(X), g(X) are

> random variables taking values in

> > R, and Corr-f-g(X) is a random variable taking values in {0,1}.

> >

> > If S is a sequence of values of X, then let Corr-f-g(S) be the

> sequence of values of Corr-f-g

> > corresponding to the sequence S of X-values.

> >

> > Define Min-1(S) to be the least place in Corr-f-g(S) containing a

> 1; and to be 0 if there is no such

> > place.

> >

> > Suppose I construct a collection of sequences S.i, each of length

> 1,000,000,000, by repeated

> > sampling from Distr(X). Suppose there are 100,000,000 sequences I

> construct.

> >

> > I can now construct the average of Min-1(S) over all the

> 1,000,000,000sequences S.i.

> >

> > All these things are mathematically well-defined.

> >

> > Now, suppose I have deterministic software, S. Let f(i) be the

> output of S on input i. Let g(i) be

> > what the specification of S says should be output by S on input

> i. Corr-f-g is the correctness

> > function of S, and Mean(Min-1(S)) will likely be very close to

> the mean time/number-of-demands to

> > failure of S if you believe the Laws of Large Numbers.

> >

> > I have no idea why you want to suggest that all this is

> nonsensical and/or wrong. It is obviously

> > quite legitimate well-defined mathematics.

> >

> > PBL

> >

> > Prof. Peter Bernard Ladkin, Faculty of Technology, University of

> Bielefeld, 33594 Bielefeld, Germany

> > Je suis Charlie

> > Tel+msg +49 (0)521 880 7319 www.rvs.uni-bielefeld.de

> <http://www.rvs.uni-bielefeld.de>

> >

> >

> >

> >

> > _______________________________________________

> > The System Safety Mailing List

> > systemsafety_at_xxxxxx > <mailto:systemsafety_at_xxxxxx >

> --

> David Haworth B.Sc.(Hons.), OS Kernel Developer

> Tel: +49 9131 7701-6154 <tel:%2B49%209131%207701-6154> Fax:

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> <http://keyserver.pgp.com>

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> Fürth HRB 4886

>

> Disclaimer: my opinion, not necessarily that of my employer.

>

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>

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-- Peter Bishop Chief Scientist Adelard LLP Exmouth House, 3-11 Pine Street, London,EC1R 0JH http://www.adelard.com Recep: +44-(0)20-7832 5850 Direct: +44-(0)20-7832 5855 _______________________________________________ The System Safety Mailing List systemsafety_at_xxxxxx

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