So personally I'm quite excited about the whole "multiway" point of view on non-determinism. The causal graphs that Stephen presents here are one way of summarizing how local events interact with one another across the space of possible histories, but you can go further. I'm working on a generalization of this idea, which I'm calling a token event graph, which "factors" causally distinct subsystems of a rewrite system (such as an NDTM, a hypergraph rewriting system, a string rewriting system, etc.) in a clean and precise way. While it is still early days, there is already an intriguing amount of rich mathematical structure to describe and formalize. I hope to publish a blogpost about this soon.