status for release 1.0

[Peter Cameron]

On Fri, Oct 10, 2003 at 01:38:51PM +0100, Leonard Soicher wrote:
> > 
> > The current RNC definition is:
> > 
> >     element affine_resolvable {
> > 	attribute flag { "true" | "false" | "unknown" },
> > 	attribute mu { xsd:positiveInteger } ?
> >     } ?
> > 
> > I am not sure about "unknown". Do we need it here?
> > 
> 
> If we actually have a resolution then testing the affine_resolvable
> property is not difficult.  So usually, the meat of the "unknown" for
> affine_resolvable would be handled by the resolvable indicator.  However,
> experts, could we have the case where we know (say for theoretical
> reasons) that our design is resolvable but not whether it is affine
> resolvable? if in doubt, we should leave the possibility "unknown"
> for affine_resolvable.
>
It is much cheaper to test whether a design is affine resolvable than
to test whether it is resolvable! (So much for atomic indicators.) If
any two blocks meet in 0 or mu points, then just test whether "equal or
meet in 0 points" is an equivalence relation on blocks.
 
> A block design consisting of a single parallel class is affine
> resolvable. In that case "mu" is not uniquely defined and should be
> left out (or not_applicable ??). For this reason, and so that we can add
> attributes such as "mu" to indicators in future releases in a backward
> compatible manner, I suggest that our semantics allow attributes such as
> "mu" not to exist even when an indicator "flag" is true.
>
True. Either mu is undefined for these, or we legislate that they are
not affine resolvable.
 
> I suggested a while ago that we might want to have an (optional)
> attribute "lambda" for the pairwise_balanced indicator (if the design is
> pairwise balanced then lambda records the non-negative constant number
> of blocks containing a pair of points).  Say:
> 
> element pairwise_balanced {
> 	attribute flag { "true" | "false" }
>   	attribute lambda { xsd:nonNegativeInteger } ?
>     } ?
> 
> Is there support for this?
>
There is support from me. There are a lot of people who are really only
interested in the case lambda=1.

Peter.