Re: LALR parsing (Torben Ęgidius Mogensen)
Thu, 10 Dec 2009 10:12:35 +0100

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From: (Torben Ęgidius Mogensen)
Newsgroups: comp.compilers
Date: Thu, 10 Dec 2009 10:12:35 +0100
Organization: Department of Computer Science, University of Copenhagen
References: 09-12-007 09-12-009 09-12-018
Keywords: parse, LALR, theory
Posted-Date: 11 Dec 2009 00:01:58 EST (Danny Dubi) writes:

>> There may well be general parsers that are faster than matrix
>> multiplication. IIRC, the lower bound for CF parsing is still O(n).

> The following paper explains that a fast parsing algorithm can be
> turned into a fast (but not AS fast, though) binary matrix
> multiplication algorithm.

> author = {Lee, Lillian},
> title = {Fast context-free grammar parsing requires fast
> boolean matrix multiplication},

I read the abstract of that paper some time ago, and as far as I recall,
the essense is that you can multiply two sqrt(n) x sqrt(n) binary
matrices in the time it takes to parse a length-n string. So if you can
multiply binary matrices in O(n^2) time, you _might_ be able to parse in
linear time. But having only read the abstract, I can't say for sure.

Also, there may be difference between parsing (constructing a
derivation) and recognition (deciding membership). It is plausible that
you can do the latter faster.


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