13 Dec
2020
13 Dec
'20
12:39 a.m.
On Sun, Dec 13, 2020 at 12:19:18AM -0500, Carter Schonwald wrote:
Having a decidable equality seems important for reasoning about groups. Or computing on representations thereof.
This is of course not always possible. If a group is presented as a quotient of a free group on a set of generators via some set of relators, then deciding whether two words are equal is IIRC known to be generally intractable. One can still perform the group operation, but there is no known terminating algorithm for constructing a canonical form for an element, performing equality tests, ... Of course one might take the view that groups where equality is not computable are not "useful", but that might rule out some applications. -- Viktor.