2026-10-31T23:09:57Z https://nostr.now Steven Schaefer https://nostr.now/npub1s8lg6tupxh4sdjuqufsd2ze8evu3fdu6fwvzwj4nn6cpqtcu4p5sss6fln https://media.mathstodon.xyz/accounts/avatars/111/959/149/866/531/093/original/ae21df2f49b02587.jpeg https://media.mathstodon.xyz/accounts/avatars/111/959/149/866/531/093/original/ae21df2f49b02587.jpeg https://nostr.now/nevent1qqs9spaddxnhmqqch46fmq3nhyqq7mjhrll7nl38slnmtp9n98ppduszyzqlarf0sy67kpktsr3xp4gtyl9nj99hnf9esf62kw0tqyp0rj5xj6panvz In reply to <a href='/nevent1qqswv6u0fwcxx32eprff2jjqz8ha5p6pmmdc7f943e64frfgqn9uytqedpv47'>nevent1q…pv47</a><br/>_________________________<br/><br/>I was looking at these coalgebras a couple months ago, and their relationship to regular languages had me very curious<br/><br/>If I recall, the finite coalgebras in this system correspond to regular languages through a version of Kleenes theorem. I think similar characterizations can be made for context free languages, but I can’t remember precisely <br/><br/>What really strikes me is that generative grammars are inductive in nature, say through a regex or the productions of a CFG. In this setting, the inductive stuff arises as the finitary coalgebraic stuff.<br/><br/>Based solely on vibes, this feels simultaneously obvious and mind boggling! I am very curious how generally the statement “finiteness + coinduction = induction” holds? <br/><br/>There is perhaps some subtlety in the grammatical example because the labeled transition system is guaranteed to consume a character with each transition. So maybe my desired goal has to be rewritten to take into account linearity and productivity? 2025-03-15T02:49:55Z