I wonder if it is possible to have special chess engines that compete in composing chess studies.
The idea is that the engine gets some final position that is the end of the study and need to compose a correct study as long as possible that end in the final position.
Correct study is a study when white has some target to win or to draw(based on the final position) when in every move white has only a single legal move to achieve the target.
Engines may also compete in correct mate problems based on a known final position that are as long as possible that end in some position when a correct mate problem is a mate problem when always in the main line the side to move has a single move to mate in the minimal number of moves when the opponent always is going to choose one of the best moves in the main line.
Correct mate problem may allow a slower win so it is not always a correct study.
There can be also a competition between engines in composing correct problems that are also correct studies that end in a specific positions.
Engines need some good backward generator in order to calculate composing mate problems or studies.
Note that some studies may be hard to prove because you may not be sure if +1.2 of the engine in analysis is theoretical win or draw.
If the engines get limited time to compose studies in a competition they may decide to have wrong assumptions like the assumption that +5 by the engine is a win for white when longer analysis may discover that the engine is wrong.
It may be better for the engines to take some risk of composing wrong studies in order to win a competition because it is better to have 90% of the studies correct but beat other engines in 70% of the cases and not 100% of the studies correct but lose against other engines that make longer studies in 70% of the cases.
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