It looks like "Verification of Identities" by Rajagoplan and Schulman seems to be the best algorithm known: http://citeseerx.ist.psu.edu/viewdoc/download;jsessionid=A29F9C99B65004A490D... On Tue, Aug 19, 2014 at 7:21 PM, W. Edwin Clark <wclark@mail.usf.edu> wrote:
The word you want is semigroup: http://en.wikipedia.org/wiki/Semigroup
Well, there is this: http://en.wikipedia.org/wiki/Light's_associativity_test
And you might find something of interest in the reference to this OEIS entry: number of semigroups of order n http://oeis.org/A001423
On Tue, Aug 19, 2014 at 9:02 PM, Henry Baker <hbaker1@pipeline.com> wrote:
I'm interested in binary operations on a finite set S that are associative, period; no other constraints.
1. Are there "fast" methods for checking associativity given the operation table?
2. Can all such associative operations be emulated "efficiently" using an isomorphism in which the operation is matrix multiplication (not just over standard rings, but extended like Knuth & the APL language do) ?
(RCS knows why I'm asking this question.)
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