I've recently been paying attention to community theoretical computer science forums, including on sites such as StackExchange. This question recently came up:
Are PSPACE-complete problems inherently less tractable than NP-complete problems?
Naturally, since we don't know whether PSPACE is not equal to NP, there is not yet a formal answer to this question. Intuitively, however, this becomes a question of whether it is harder to figure out which player can win a game than to find the solution to a (one-player) puzzle. The link above provides a wonderful bunch of points, but let me mention a few specifically. :)
* Ryan Williams notes that some randomized game tree solvers are very effective, and perhaps solving games isn't quite as terrifying as many might think.
* Neil de Beaudrap notes that verifying solutions is still extremely important, which we know how to do for NP-complete problems. Aaron Sterling backs this up with a great comment about humans being able to remember and describe proofs.
* Lance Fortnow points out that we know how to create average-case PSPACE-complete problems, but don't yet know how to do this for NP.
* Suresh Venkat mentions that in practice, NP-solvers are actually often very fast, and NP-completeness is not always seen as a barrier to computing.
This is one of the few questions on the forum that I have actually read multiple answers to, and it's one I feel I can read over and over. Personally, I find it hard to believe that PSPACE isn't much harder than NP, and professionally I'm partly banking on it by spending my time finding PSPACE-complete games!
A Waterfall of my Feelings
1 month ago