[Retros] solution independence

[Andrew Buchanan]

Francois Labelle wrote:


> I get the feeling that solution independence is not a yes/no concept like

> "being cooked", but that it's continuous and subjective. And I doubt that

> you could describe mathematically what you're looking for without a good 5

> rounds of trial and error, but you can try!


I agree that there are degrees of solution independence, and we can't be
completely prescriptive, but there are some things we can say.

(1) If two solutions have all the same moves, but in a different order, then
the problem is absolutely cooked.
(2) For me, if every unit has a different trajectory between the two
solutions, then the solutions are absolutely independent. By "a different
trajectory" I mean that if unit M occupies square p in one solution, it may
not occupy it in the other, unless it is the starting square of the unit or
its destination square if it survives. If a unit M is captured in both
solutions, then it must be captured on different squares.
(3) And then there are a whole mass of cases which are intermediate to these
two extremes. In the end it's a matter of aesthetics which of these is OK.
To some extent, this depends on what is the content of the SPG: if it's
successful at its aim, then some overlap between solutions maybe allowable.

Thanks to Francois Labelle's work, we have an embarrassment of riches in
terms of multi-solution SPGs being unearthed, and the focus perhaps now
needs to shift to "data mining" tools, since that's the limiting factor. Why
not pass all the multiple solution SPGs generated by Francois into Euclide
(which has a Batch mode). Euclide will also flag up the differences between
the different solutions unearthed, so it's easy to see by eye which are the
cooks, and where there is clear difference. Natch and Popeye may also have
capabilities here.

Related questions are:
- how closely one SPG resemble another with a slightly different diagram?
- how related are the solutions if we have an SPG=n, PG=n+0.5?
- how asymmetrical are the White/Black moves which lead to a symmetric
position?

Cheers,
Andrew.