These 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.
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?
5 comments
[ 3.3 ms ] story [ 24.9 ms ] threadOne thing that I have often thought though is that the mathematical sciences could do with more cross-pollination with coalgebra.
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?
https://chat.openai.com/share/6a76cdcc-a303-4717-885c-519951...