If you read what I wrote, you'd see I never claimed originality. Anyway, that's cool. I'll need to check how much abstract algebra stuff they use.

Using semirings (uh, rigs) alone isn't impressive. Do they consider semirings with more algebraic structure attached to them?

> Using semirings (uh, rigs) alone isn't impressive. Do they consider semirings with more algebraic structure attached to them?

Wiki says they have R, the two tropical semirings, the 'max-min' semiring, and GF(2). The tropical and max-min have your idempotency requirement, all but the max-min have involution.