Abstract
Let \( R \subseteq \sum {^*}\) be a regular set. Recall from Lecture 15 that a Myhill—Nerode relation for R is an equivalence relation \( \equiv \;on\;\sum {^*} \) satisfying the following three properties:
-
(i)
≡ is a right congruence: for any x, y ∈ ∑* and a ∈∑
$$x \equiv y\; \Rightarrow \;xa \equiv ya; $$ -
(ii)
≡ refines R: for any x, y ∈∑*,
$$ x \equiv y\; \Rightarrow \left( {x \in R \Leftrightarrow y \in R} \right);$$ -
(iii)
≡ is of finite index; that is, ≡ has only finitely many equivalence classes.
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© 1977 Springer Science+Business Media New York
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Kozen, D.C. (1977). The Myhill—Nerode Theorem. In: Automata and Computability. Undergraduate Texts in Computer Science. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-85706-5_17
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DOI: https://doi.org/10.1007/978-3-642-85706-5_17
Publisher Name: Springer, Berlin, Heidelberg
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