High Quality Content by WIKIPEDIA articles! In mathematics and computer science, the syntactic monoid M(L) of a formal language L is the smallest monoid that recognizes the language L. Given S c M of a monoid M, one may define sets that consist of formal left or right inverses of elements in S. These are called quotients, and one may define right or left quotients, depending on which side one is concatenating. The syntactic quotient induces an equivalence relation on M, called the syntactic relation, or syntactic equivalence or syntactic congruence (induced by S).

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