[Retros] At home proof games in 7.0 moves

[andrew buchanan]

Joost de Heer wrote:


>[Andrew Buchanan wrote:]

>> (c) SPG without specified number of moves. This is just like a PG

>> except that the solver has to find the number of moves, which is the

>> minimum possible in which the position can be reached, and is unique.

>

> The term 'SPG' has nothing to do with uniqueness.


That is not my understanding.

A common use of the term SPG is to refer to a kind of composition. One
property of a (sound) composition is that the solution must be unique. SPG
inherits this property.

My point was that one common use of the term PG (a) does *not* involve
uniqueness. This is where the purpose of the proof game is just to
demonstrate that a position is legal. Uniqueness does not come into it.

Or one may talk about "how many proof games lead to position X".

PG may instead (b) refer to a type of composition, and here uniqueness would
be a property.

Here one may talk about e.g. "how many at-home proof games there are".

Either kind of PG may be "shortest", but definition (a) is not frequently
used in this sense. 

"PG" is analogous to the concept of "mate in 2". One may refer to a game
allowing a mate in 2. In this case, uniqueness is not an issue. However
"mate in 2" may also refer to a composition, and in this sense, must be
unique.

Hope this helps,
Andrew.