Comments on: Quote http://bit-player.org/2006/060111wheeler An amateur's outlook on computation and mathematics. Fri, 30 Jul 2010 22:32:28 +0000 http://wordpress.org/?v=2.6.3 By: Jonathan Katz http://bit-player.org/2006/060111wheeler#comment-4 Jonathan Katz Wed, 11 Jan 2006 19:03:28 +0000 http://bit-player.org/?p=9#comment-4 I always thoroughly enjoy reading your articles in American Scientist, and am looking forward to reading your blog! Speaking of which, probably someone has contacted you regarding a (slight?) mistake in your last column about Sudoku, specifically when you wrote: "For problems in NP, the effort needed grows exponentially." Of course, the class NP consists of problems whose solutions can be easily verified (this is essentially the definition of NP), but currently we do not know whether all problems in NP can be *solved* efficiently. In any case, problems in NP need not take exponential time (the class of efficiently solvable problems is a subset of NP), and even some of the "hardest" problems in NP (i.e., NP-complete problems) can be solved in sub-exponential (but super-polynomial) time. I always thoroughly enjoy reading your articles in American Scientist, and am looking forward to reading your blog!

Speaking of which, probably someone has contacted you regarding a (slight?) mistake in your last column about Sudoku, specifically when you wrote: “For problems in NP, the effort needed grows exponentially.” Of course, the class NP consists of problems whose solutions can be easily verified (this is essentially the definition of NP), but currently we do not know whether all problems in NP can be *solved* efficiently. In any case, problems in NP need not take exponential time (the class of efficiently solvable problems is a subset of NP), and even some of the “hardest” problems in NP (i.e., NP-complete problems) can be solved in sub-exponential (but super-polynomial) time.

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