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Re: LR(1) Parsing : Error Handling & Recovery

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From George Neuner <gneuner2@comcast.net>
Newsgroups comp.compilers
Subject Re: LR(1) Parsing : Error Handling & Recovery
Date Fri, 25 Jul 2014 21:58:49 -0400
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On Mon, 21 Jul 2014 06:07:55 +0000 (UTC), Chris Dodd <cdodd@acm.org>
wrote:

>George Neuner <gneuner2@comcast.net> wrote in news:14-07-041@comp.compilers:
>> LL(k) always can be refactored to single token lookahead, but it
>> causes an explosion of grammar states.  E.g., given a single LL(3)
>> rule, an equivalent set of LL(1) rules must match every valid
>> combination of tokens at +1, +2 and +3.
>
>Not true -- LL(k+1) languages are a strict superset of LL(k) languages, so
>there exist LL(k) grammars that cannot be refactored to a smaller k.

Yes and no.

For every LL(k) grammar where both k and the set T of tokens is fixed,
there is an equivalent LL(1) grammar.  In the worst case, the
equivalent LL(1) grammar will have k**T rules.

Only where k or T is unbounded, so that the power set of {n:1<=n<=k}
lookahead tokens for some rule is not enumerable, can you not derive
an equivalent in LL(1).

The problem is that an LL({n:1<n<=k}) rule explodes multiplicatively
into an n-level tree of LL(1) rules, with each branch at each level
m<=n having to cover follow(m).

Meaning that it is effectively unworkable for any but small k.

Fortunately, for any reasonable LL(k>1) grammar, k will be bounded and
small, and the grammar will contain just a handful of rules requiring
the maximum k lookahead.  Most rules will be LL({n:1<=n<k}) where n is
very small.

George

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Thread

LR(1) Parsing : Error Handling & Recovery Seima Rao <seimarao@gmail.com> - 2014-07-10 05:30 +0530
  Re: LR(1) Parsing : Error Handling & Recovery Ivan Godard <ivan@ootbcomp.com> - 2014-07-16 16:39 -0400
    Re: LR(1) Parsing : Error Handling & Recovery Evangelos Drikos <drikosev@otenet.gr> - 2014-07-17 20:15 +0300
      Re: LR(1) Parsing : Error Handling & Recovery Ivan Godard <ivan@ootbcomp.com> - 2014-07-17 13:03 -0700
        Re: LR(1) Parsing : Error Handling & Recovery Ivan Godard <ivan@ootbcomp.com> - 2014-07-17 13:57 -0700
          Re: LR(1) Parsing : Error Handling & Recovery wclodius@earthlink.net (William Clodius) - 2014-07-18 13:41 -0600
            Re: LR(1) Parsing : Error Handling & Recovery Stefan Monnier <monnier@iro.umontreal.ca> - 2014-07-18 21:09 -0400
              Re: LR(1) Parsing : Error Handling & Recovery Hans-Peter Diettrich <DrDiettrich1@aol.com> - 2014-07-19 12:04 +0200
                Re: LR(1) Parsing : Error Handling & Recovery Stefan Monnier <monnier@iro.umontreal.ca> - 2014-07-20 10:28 -0400
                Re: LR(1) Parsing : Error Handling & Recovery Hans-Peter Diettrich <DrDiettrich1@netscape.net> - 2014-07-21 10:46 +0200
                Re: LR(1) Parsing : Error Handling & Recovery Stefan Monnier <monnier@iro.umontreal.ca> - 2014-08-06 21:32 -0400
            Re: LR(1) Parsing : Error Handling & Recovery arnold@skeeve.com (Aharon Robbins) - 2014-07-20 06:05 +0000
    Re: LR(1) Parsing : Error Handling & Recovery George Neuner <gneuner2@comcast.net> - 2014-07-17 18:49 -0400
      Re: LR(1) Parsing : Error Handling & Recovery wclodius@earthlink.net (William Clodius) - 2014-07-18 13:41 -0600
        Re: LR(1) Parsing : Error Handling & Recovery Hans Aberg <haberg-news@telia.com> - 2014-07-19 15:29 +0200
          Re: LR(1) Parsing : Error Handling & Recovery Evangelos Drikos <drikosev@otenet.gr> - 2014-07-20 00:40 +0300
            Re: LR(1) Parsing : Error Handling & Recovery Hans Aberg <haberg-news@telia.com> - 2014-07-20 01:38 +0200
              Re: LR(1) Parsing : Error Handling & Recovery Evangelos Drikos <drikosev@otenet.gr> - 2014-07-21 15:20 +0300
                Re: LR(1) Parsing : Error Handling & Recovery Hans Aberg <haberg-news@telia.com> - 2014-07-21 18:39 +0200
                Re: LR(1) Parsing : Error Handling & Recovery Evangelos Drikos <drikosev@otenet.gr> - 2014-08-26 13:44 +0300
                Re: LR(1) Parsing : Error Handling & Recovery Hans Aberg <haberg-news@telia.com> - 2014-08-29 11:13 +0200
                Re: split tokens; was LR(1) Parsing : Error Handling & Recovery Evangelos Drikos <drikosev@otenet.gr> - 2014-09-03 16:57 +0300
                Re: LR(1) Parsing : Error Handling & Recovery Hans Aberg <haberg-news@telia.com> - 2014-09-03 19:07 +0200
        Re: LR(1) Parsing : Error Handling & Recovery George Neuner <gneuner2@comcast.net> - 2014-07-20 01:19 -0400
          Re: LR(1) Parsing : Error Handling & Recovery wclodius@earthlink.net (William Clodius) - 2014-07-20 21:43 -0600
            Re: LR(1) Parsing : Error Handling & Recovery wclodius@earthlink.net (William Clodius) - 2014-07-21 21:44 -0600
          Re: LR(1) Parsing : Error Handling & Recovery Chris Dodd <cdodd@acm.org> - 2014-07-21 06:07 +0000
            Re: LR(1) Parsing : Error Handling & Recovery George Neuner <gneuner2@comcast.net> - 2014-07-25 21:58 -0400
              Re: LR(1) Parsing : Error Handling & Recovery Chris Dodd <cdodd@acm.org> - 2014-07-26 21:16 +0000
                Re: LR(1) Parsing : Error Handling & Recovery Hans-Peter Diettrich <DrDiettrich1@netscape.net> - 2014-07-28 14:43 +0200
                Re: LR(1) Parsing : Error Handling & Recovery Chris Dodd <cdodd@acm.org> - 2014-07-29 19:38 +0000
  Re: LR(1) Parsing : Error Handling & Recovery Eric <news@fx29.iad.highwinds-media.com> - 2014-07-16 16:40 -0400

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