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I have brought back the simple summary and have fixed a typo in it. I have also renamed the 'formal' definition to 'explicit' definition per your suggestion, which I agree with.
:Hello, I think you misunderstood my comment - I don't hold anything against anonymous editors, and I respect your right to anonymity. I just wanted to identify the edit I was talking about.
:As I said, it is quite reasonable to ask for a simpler first sentence. But I maintain that your first sentence was far too simple, to the extent that it was wrong. A great many important nondeterminstic algorithms do not return different results for a fixed input. These kinds of algorithms are really important in the study of nondeterminstic polynomial time, in complexity theory. This is one of the main fields of computer science where nondeterminstic algorithms are important. I'm not sure how familiar you are with this.
:In line with this, I have tried to correct and improve the opening first sentence. I hope its clearer than the longer paragraph, without being misleading. It's still not perfect, I admit. (In case you find I don't reply to any further discussion: I'll be away now for a few days.) I also changed 'explicit' to 'detailed', since I think that is more appropriate. All the best, [[User:Sam Staton|Sam Staton]] 08:42, 18 October 2007 (UTC)
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