On the other hand, proving that you have solved it is much harder than actually solving it (as in never making a losing mistake). 8x8 chess is an extremely large instance, vastly bigger than checkers. Exptime problems are solved on a daily basis, even large instances. That said, it's important to know that even intractable (exptime) does not mean impossible. You know it's going to be incredibly hard if it's exptime. However, the complexity class is a very good shorthand for explaining how difficult a problem may be to solve. Have, in fact, said as much about the complexity of deciding winning positions inĬhess as the tools of reduction and completeness in computational complexity allowįrom the point of view of computational complexity a game on a fixed size of board is a finite problem that can be solved in O(1), for example by a look-up table from positions to the best move in each position. Thus, while we may have said very little if anything about 8x8 chess, we Technically it does not "work" for either, since complexity theory is about how the time or space of functions grow as the input variable grows, and here we are talking about fixed board sizes. Please continue to give us your feedback and suggestions on how we can help make /r/chess better for everyone. Use the message the moderators link if your posts or comments don't appear, or for help with any administrative matters. Twitter/Facebook posts must contain a direct link to the tweet/post, and include the author's nameĬhess Spoiler format for problem answers etc., Instructions for /r/chess PGN addon ( Chrome, Firefox)ĭon’t engage in abusive, discriminatory, or bigoted behavior.ĭon't ask for advice about ongoing games.ĭon’t spoil tournament results in submission titlesĭo not use /r/chess exclusively to promote your own content. News Puzzles Games Strategy Twitch Other Resources
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