The Dyck language I was already aware of; I linked it in the previous post in the series. But the bicyclic semigroup was new to me. Yes, the bones of it are very similar to my "stack monoid;" if you erase the actual element values of the stack contents and just count the lengths, it's clearly the same thing. No doubt there's some theory that justifies adding the elements back in as well.
I'll have to check out the Kmett talk - from the description it sounds very interesting.
I'll have to check out the Kmett talk - from the description it sounds very interesting.