Newsgroups: sci.lang
Path: cantaloupe.srv.cs.cmu.edu!das-news2.harvard.edu!news2.near.net!news.mathworks.com!yeshua.marcam.com!charnel.ecst.csuchico.edu!olivea!news.hal.COM!decwrl!netcomsv!netcom.com!smryan
From: smryan@netcom.com (S M Ryan)
Subject: Re: Procrustean linguistics (was: Ferengi Language)
Message-ID: <smryanCy9rq0.Kr0@netcom.com>
Organization: Dawn Patrol on the Internet
X-Newsreader: TIN [version 1.2 PL1]
References: <372f0l$p0d@mother.usf.edu> <374h7s$he9@tardis.trl.OZ.AU> <ONEIL.94Oct25140444@fas.harvard.edu>
Date: Wed, 26 Oct 1994 07:34:47 GMT
Lines: 44

: >>However, extracting patterns in a general setting will yield
: >>(literally) an infinite number of patterns
: >  ^^^^^^^^^     ^^^^^^^^
: >
: >  Literally for the numerically unwashed. The lexical inventory
: >  of a language being finite, and its speakers being mortal,
: >  the number of possible different utterances is finite.

: Wrong.  Any given speaker will only choose to utter a finite number of
: them, but nonetheless there is no way to limit the cardinality of the
: set of utterances that speaker could speak and understand to a finite
: number.

Wrong. Or right. I would recommend not worrying about the precise
meanings of 'infinite' or 'literally infinite' or 'cardinality.' 

The cardinality of the set of the extracted patterns must be no
greater than the set of patterns, but what is the set of patterns?
Do you mean the set of strings generated by Turing machine in finite
unbounded time? Finite bounded time? A recursive set or re set?
Or is the set noncomputable with cardinality greater than aleph-zero.

That forms the upper limit on the cardinality of extracted patterns.
The lower bound? 0? 1? How much work do you want to do?

Bounded does not mean finite, unbounded does not mean infinite. 
Bounded means I give you some number which is greater than all the 
space or time you would need. Unbounded means I can't. Given a type 
1 grammar and the length of the input string (not its contents), I 
can give you a finite bound on how many steps it will need to accept 
a string. For a type 0 grammar and the length of the input, I only 
know it will accept in a finite but unbounded number of steps.

And it might take a transfinite number of steps to reject it.

And I wouldn't be surprised if hardly anybody cares about such
distinctions, which is why I would recommend not worrying about the
precise meanings.

-- 
 _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ __________________________________
| | | | | | | | | | | | | | | | | | | | | smryan@netcom.com	PO Box 1563
| | | | | | |G|A|T|E| |1| | | | | | | | |             Cupertino, California
|Electricians use gate 2| | | | | | | | |_(xxx)xxx-xxxx_______________95013
|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|____(coming soon: a new signature)
