Aggregation and Tiling as Multicomputational Processes
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Aggregation and Tiling as Multicomputational Processes
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Re: Aggregation and Tiling as Multicomputational Processes
#2Re: Aggregation and Tiling as Multicomputational Processes
#3These 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.
Re: Aggregation and Tiling as Multicomputational Processes
#4These 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…
Wow, 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?
Re: Aggregation and Tiling as Multicomputational Processes
#5These 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…
Wow, 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…
I'd love to see both an answer to your question, and also your twenty minute explanation written up, if you haven't already!
Re: Aggregation and Tiling as Multicomputational Processes
#6Earlier quoted context omitted.
Wow, 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…
I'd love to see both an answer to your question, and also your twenty minute explanation written up, if you haven't already!
I 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-519951...