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Re: Set of strings reducing problem

• To: mathgroup at smc.vnet.net
• Subject: [mg58578] Re: [mg58560] Set of strings reducing problem
• From: "Edson Ferreira" <edsferr at uol.com.br>
• Date: Fri, 8 Jul 2005 00:46:09 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

> Hi, Edson,
> 
> I guess I have a basic question on your transformations. You give six
> rules for how to "add" the differing characters; are these the only
> combinations possible?

Yes! Those are the only possible combinations!

>For example, will the combination of strings of
> "1111M111"
> + "11112111"
> ever be encountered? 

Never!

>In addition, when you say that the strings will
> differ from each other by only one character, does this mean in _one_
> given position? 

Yes! The two strings that will be "joined" have only one different charac=
ter at same position!


>For example, a transpose of characters as in
> "21111111" vs. "11111112" might be seen as two strings 
> with only one differing character, or two strings of _two_ differing
> characters (one at either end).

You can't join those examples!

> 
> From your statement of applying transformation rules repeatedly
> until nothing changes, my guess is that, yes, you've given the complete=

> set of transformation rules. 

Yes! The rules are only those I gave!

>In this case, what happens if I try to
> "decompose" (someone more familiar with string manipulations, and,
> perhaps, crytanalysis or group theory, may be better suited to ask thes=
e
> questions) the operations? Can I, for example, do something like
> 
> 1 + X = D
> ==>1 + D = 1+(1+X)
> =(1+1) +X
> =1 + X <--- Here I've assumed that because you want
> strings differing by characters, that (1+1) -> 1.
> In other words, is the "addition" associative? I think the answer to
> this hinges on the answer as to the "only one character" problem.

Yes! they are associative AND comutative! But all possible cases were men=
tioned on the rules!


> 
> 
> Interesting problem! I'm sorry I can't help
> (yet) on the implementation.
> C.O.
> 

Thank you very much anyway!

> Edson Ferreira wrote:
> 
> >Dear Mathematica Users,
> >
> >I have a problem that I haven't got any clue to solve with Mathematica=