Uh (first off) its the german sense of vertex, not the anglo sense lol
(Image Search for “3-gluon vertex” to get a language independent sense)
On (regrettably still halfass’d) reflection,there are necessary subtleties which your question is stalking but it will take me a few days or weeks to page in
(but now I'm reminded —physics envy, mind you— of a "renormalisation" in regex engines. Recall the definition of A*:
A* == ϵ | A | A*A*
Mathematically, it doesn't make any difference if A also matches epsilon. However, when generating code, if it does, it's very useful to treat the above
as asking for:
A* == ϵ ⨁ A† ⨁ (A*A*)†
where A† recognises only the nondegenerate, "squarefree", portion of A.
Otherwise one risks getting stuck recognising ϵ an infinite number of times (leaving squares in is harmless); anyway the presence of the ϵ means that during* recognition of A*, there is one incoming edge but two outgoing.)
* speaking in terms of left to right traversal, but we can also go right to left, which (by a folk theorem) means we can also calculate bottom up. I'll have to reflect upon what A* might produce, edgewise, in that last case.
Mutual envy hits the sweet spot imho.. to me the (median) Informatiker has superior naming/notation/training. Recall that bit with Moitra et al cutting the Gordian knot of thermalization vs entanglement. (That dude couldnt touch-type to save his bacon, pls forgive the (reverent) gossip)
Here: how far is this regex from non-associativity.
[& this connection is exactly what i was hoping for! I’d hoped the regular in regularity structs would trigger smth, & save us both weeks (of procrastination, in my case)]
Was i born decades earlier, i might have wandered into a VC “human capital destruction” job, since i have a roughly equivalent mix of traits..
The binary ops, sequencing and alternation are associative (monoidal).
The unary op, kleene star, blocks reassociation.
However, it is occasionally useful to use the associative-adjacent identity A;A* == A*;A (and more generally, A^n;A* == A*;A^n;A* == A*;A^n == ...)
A Chirurg, an Architekt, and an Informatiker are discussing whose profession has the most patina. The Chirurg points out that when God removed Adam's rib to form Eve, He was doing surgery. The Architekt points out that when God made Heaven and Earth out of the Chaos, He was doing architecture. The Informatiker just smiles broadly and then asks, "Und? where then think you the Chaos came from? a cereal Gimmick?"
are these triangles determinate, or is there a search process involved?
(maybe I ought to be looking for "ghost faces" that'd simplify my existing edge & vertex model of computation?)