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feat(Language): characterizing regular languages as preimages of subsets of finite monoids - #921

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ctchou wants to merge 2 commits into
leanprover:mainfrom
ctchou:finite-monoid
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ctchou wants to merge 2 commits into
leanprover:mainfrom
ctchou:finite-monoid

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@ctchou

@ctchou ctchou commented Sep 18, 2026

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This PR develops yet another characterization of regular languages:

A language is regular if and only if it is the preimage of a subset of a finite monoid M under a monoid homomorphism from the free monoid on its alphabet to M.

@ctchou

ctchou commented Sep 20, 2026

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Now that #903 is merged, this PR is ready for review.

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