RobertJasiek wrote:
Quote:
There are NO redefinitions of J2003-terms.
Maybe I use definition in a broader sense than you: Something determined by an algorithm can be also considered to be defined by it.
Let me express it a bit differently: Given the definitions in J2003 and the algorithms, I want to see propositions proven of this kind: "The algorithm A determines the strings fitting definition D."
Why do you want to have "proven" something that is an inherent feature of the minimax-algorithm ?
The minimax-algorithm transports the leaves' statuses via branching point after branching point to the root of the variation tree.
In the end you have the root's status as the concluding status of the string's evaluation.
There must be at least one leaf, which has this concluding status.
Highlight the path between neighbouring branching points (including root and leaves), which habe this concluding status, and you will have marked everything that is "forced".
If the concluding status is A (string remains on the board), this is forced by the player. So it cannot be forced by the opponent. This equals the definition of "uncapturable".
If the concluding status is B2 (string has been captured, successor on local-1), it is forced by the opponent that there is no status A surviving. Thereafter the best status that can be reached from the player's standpoint is B2. This status is reached, so it is forced by the player that there is a successor. The opponent cannot force no successor. This equals the definition of "capturable-1".
If the concluding status is B31 (string has been captured, no successor on local-1, permanent stone on local-2\1), it is forced by the opponent that there are no statuses A or B2 surviving. Thereafter the best status that can be reached from the player's standpoint is B31. This status is reached, so it is forced by the player that there is a permanent stone on local-2\1. The opponoent cannot force no permanent stone on local-2\1. This equals the definition of "capturable-2\1".
Local-2\1 is part of local-2, so this equals the definition of "capturable-2", too.
If the concluding status is B32, it is forced by the opponent that there are no statuses A, B2, or B31 surviving. So it is forced by the opponent that the string is "not alive".
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The really most difficult Go problem ever:
https://igohatsuyoron120.de/index.htmIgo Hatsuyōron #120 (really solved by KataGo)