Hi,

But you're asking for a third piece of information.  If you query for
> "foo bar baz" and I can tell you that it will never extend to "* foo bar
> baz" for any word * (due to pruning or filtering), then you need only
> remember "foo bar" (or even less).  The trie knows this but because the
> pointers are equal but it currently isn't telling you.  Probing could
> tell you this if I used the otherwise-unused probability sign bit to
> encode it.
>

The thinking is here, given a prefix of "A B C D" and a language model
of order 5, then we can ignore D if the ngram "A B C" is unknown.

Why? Because if "A B C" is unknown, then also any "* A B C" will be
unknown, assuming sane low-count pruning. So, there will always be
free back-off to the lower order n-gram.

Knowing that there is no "* A B C D" is the language model may
not be helpful, since different "* A B C" have different backoff costs.

-phi
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