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- Newsgroups: comp.theory.cell-automata
- Path: sparky!uunet!think.com!sdd.hp.com!cs.utexas.edu!hellgate.utah.edu!asylum.cs.utah.edu!tolman
- From: tolman%asylum.cs.utah.edu@cs.utah.edu (Kenneth Tolman)
- Subject: Re: commuting CA rules
- Date: 10 Nov 92 13:56:54 MST
- Message-ID: <1992Nov10.135655.10314@hellgate.utah.edu>
- Keywords: cellular automata, commutation of rules
- Organization: University of Utah, CompSci Dept
- References: <2468@aupair.cs.athabascau.ca>
- Lines: 19
-
- > Given a global CA rule F:E-->E it is possible to find a set of
- >non-linear Diophantine equations whose solution set determines all
- >rules (of a given neighborhood size) which commute with F.
- >(Commutation of Cellular Automata Rules, Burton Voorhees, preprint)
- >
- >Is anybody aware of a use for this information, other than as a bit
- >of interesting theory?
-
- The major use of such tidbit is that it ties together previously?
- uncoupled domains. Proving something equivalent to something else is
- meaningless in and of itself, unless you know something (or think you could
- figure something) in the other domain that it maps into. This particular
- tidbit probably has some important ramifications... Diophantine equations
- have been studied for thousands of years, and there are many results
- about unsolvability and so forth. The trick is to learn (or find someone)
- that knows a lot about previous results for Diophantine equations and then
- use these results to say things about CA. Finding isomorphisms in general
- is very important for advancement, because it allows one to consider things
- in another light.
-