[SystemSafety] COTS display certification

[Peter Bishop]

Well I did say *in principle* (i.e. ignoring memory constraint issues).

The main point I was trying to make is that we need equivalent levels of
assurance for code and data. And assurance of data integrity needs more
coverage in standards.

Peter B

PS Your impossibility argument works if you assume Size (RVN) = size(M),
but you could could choose size(RVN) to be *less than* size(M), i.e. use
a coarser discretisation to ensure the lookup table fits the available
space.

On 27/07/2016 09:09, Peter Bernard Ladkin wrote:
> 
> 
> On 2016-07-27 08:37 , Peter Bishop wrote:
>> In principle, any input/output function could be implemented as a very
>> large lookup table. 
> 
> Not really.
> 
> Suppose machine M has memory Mem. Let RVF be a computable real-valued function RVF of real
> arguments. The domain and range values of RVF can be approximated where necessary by discrete
> rational numbers. The number of discrete rational numbers available is bounded by Size(M). Pick such
> a set, RN. Size(RN) = Size(M).
> 
> Any look-up table T in Mem for a function F has to contain Dom(F) and also Ran(F). Assuming neither
> of Dom(F) and Ran(F) is empty, then Size(Dom(F)) < Size(Mem). Which means that Dom(F) must be
> smaller than RN. It follows that at least one value in RN cannot be in Dom(F).
> 
> Let F be RVF. Let a value in RN not in Dom(RVF) be V. The pair <V, RVF(V)> is not in T. Thus T does
> not implement RVF.
> 
> Recall that is so for any lookup table T.
> 
>> What data validation techniques are appropriate
>> to a given SIL?
> 
> https://www.amazon.de/Safety-Guidance-Initiative-Working-Group/dp/1519533578
> 
> DSIWG members Dave Banham or Mike Parsons could probably answer this specific question for us.
> 
> PBL
> 
> Prof. Peter Bernard Ladkin, Bielefeld, Germany
> MoreInCommon
> Je suis Charlie
> Tel+msg +49 (0)521 880 7319  www.rvs-bi.de
> 
> 
> 
> 
> 
> 
> 
> _______________________________________________
> The System Safety Mailing List
> systemsafety at TechFak.Uni-Bielefeld.DE
> 

-- 

Peter Bishop
Chief Scientist
Adelard LLP
Eagle House, 167 City Road, London, EC1V 1AW
http://www.adelard.com
Recep:  +44-(0)20-7832 5850
Direct: +44-(0)20-7832 5855

Registered office: Stourside Place, Station Road, Ashford, Kent TN12 1PP
Registered in England & Wales no. OC 304551. VAT no. 454 489808

This e-mail, and any attachments, is confidential and for the use of
the addressee only. If you are not the intended recipient, please
telephone 020 7832 5850. We do not accept legal responsibility for
this e-mail or any viruses.