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Date: Mon, 24 Sep 2007 17:14:07 +0000

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Date: Mon, 24 Sep 2007 17:14:07 +0000

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http://www.w3.org/Bugs/Public/show_bug.cgi?id=2249 ------- Comment #5 from cmsmcq@w3.org 2007-09-24 17:14 ------- Comment #4 suggests deleting the words 'finite-length' from the description of anyURI's lexical forms and from similar passages elsewhere. That seems to me at best a risky idea. It's true that no implementation we know how to build will be able to distinguish the set of finite-length sequences from the set of infinite sequences. But I think the stipulation that the sequence of characters be finite has another utility: it helps ensure that the question "is this string in the lexical space of this datatype?" can be answered in finite time. For arbitrary strings of finite length, and arbitrary grammars of finite size, there are algorithms which can decide whether the string is recognized by the grammar. I do not believe the same is true for infinite strings. (At least, not if we accept the view that to be an algorithm, a computational method must always terminate after a finite number of steps.) So I do not think it would be wise to define the lexical spaces of any of our simple types as including infinite-length strings. It's not solely a practical question; it's also a theoretical question. (It's true that some students of automata theory have worked with automatata with infinite numbers of states, and that two-level [van Wijngaarden] grammars correspond to context-free grammars with infinite numbers of productions. But in both of these cases, I think, the existence of an algorithm for recognizing strings depends crucially upon the strings' being finite in length. In recognizing a finite-length string, even an infinite state machine or grammar can successfully be represented by a finite machine or grammar which produces the same result for this particular string. I am not a computer scientist, and I have not taken the time this morning to re-read my textbooks on this subject, so I could be wrong. So I will offer this weaker argument: almost all the textbooks I have seen describe algorithms for recognizing finite-length, not infinite strings. In view of the finiteness of any actual machine available to us, it seems unnecessary to require that implementors replace the textbook algorithms with others capable of handling infinite inputs.)Received on Monday, 24 September 2007 17:14:16 UTC

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