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=