Decidability of chess on an infinite board
The recent question Do there exist chess positions that require exponentially many moves to reach? of Tim Chow reminds me of a problem I have been interested in. Is chess with finitely many men on an...
View ArticleAnswer by Carl Mummert for Decidability of chess on an infinite board
There's no such algorithm under at least one rigorous specification of the question. Consider a position in which there is a black king at (0,0) and no other black pieces; white rooks at $(1,5)$ and...
View ArticleAnswer by Dan Brumleve for Decidability of chess on an infinite board
Yes. There is a finite board size that has essentially the same solution structure as all larger boards and an infinite board, and we can find it by solving the game completely for increasing board...
View ArticleAnswer by Dan Brumleve for Decidability of chess on an infinite board
Yes, because any chess position can be translated into Presburger arithmetic. For a fixed initial combination of piece types, let's define a position to consist of an (x, y) location for each piece as...
View ArticleAnswer by domotorp for Decidability of chess on an infinite board
I would like to convince everyone that this problem is undecidable. I cannot prove it for chess, as I lack the ability to design certain configurations but I think they must exist. And even if they...
View ArticleAnswer by Joel David Hamkins for Decidability of chess on an infinite board
There is a positive solution for the decidability of the mate-in-$n$ version of the problem. Many of us are familiar with the White to mate in 3variety of chess problems, and we may consider the...
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