4 ms·
Aggregation and Tiling as Multicomputational Processes
- uticus 3y agoRelated https://news.ycombinator.com/item?id=38188759 https://news.ycombinator.com/item?id=38188759
- tsmithe 3y agoThese general "multicomputational processes" are well known in computer science as nondeterministic transition systems, or coalgebras for the powerset functor. And in that setting there is a lot of work that has been done about the kinds of logical statement that can be said about their evolution -- such as whether a given proposition about the states may always or eventually hold; this is coalgebraic modal logic. As usual, Wolfram does not mention this prior work. One thing that I have often thought though is that the mathematical sciences could do with more cross-pollination with coalgebra.
- Syzygies 3y agoWow, thank you. So I adhere to the Schützenberger view of automata theory, that the way to explain a semester's finite automata theory to a math major in twenty minutes is via rational power series on noncommuting variables. Change the semiring from true/false to probabilities and one gets hidden Markov chain theory. So how do nondeterministic transition systems fit into this picture? I'm guessing that the connection should blow my mind with a new way to see power series?
- kian 3y agoI'd love to see both an answer to your question, and also your twenty minute explanation written up, if you haven't already!
- brylie 3y agoI have no idea what all of this means, but would like to share a GPT-4 discussion that might illuminate your request. https://chat.openai.com/share/6a76cdcc-a303-4717-885c-519951a9bb13 https://chat.openai.com/share/6a76cdcc-a303-4717-885c-519951...