feat(Language): characterizing regular languages using syntactic monoids - #903
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feat(Language): characterizing regular languages using syntactic monoids#903ctchou wants to merge 1 commit into
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ctchou
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chenson2018,
fmontesi,
kim-em and
sorrachai
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September 14, 2026 03:53
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This PR develops yet another characterization of regular languages: a language is regular if and only if its syntactic monoid is finite. The syntactic monoid is the quotient of the free monoid by the Myhill congruence, which is a two-sided congruence on finite words that is finer than the Nerode congruence used in the Myhill-Nerode theorem.
As part of this PR, both left and two-sided congruences on finite words are defined and all congruences on finite words are moved from the namespace
Cslibto the more appropriate namespaceLanguage.