“Nerode equivalence”的概念、定义、翻译、参考文献-科学参考

Nerode equivalence

Computer

An equivalence relation, =_N, arising in formal language theory. It is defined analogously to the Myhill equivalence by the weaker properties:
$\begin{array}{l} for a language L over Σ, \\ u =_{N} u' \\ if, for all w in Σ^{*}, \\ u w \in L iff u' w \in L \\ and for a function f, \\ u =_{N} u' \\ if, for all w in Σ^{*}, \\ f (u w) = f (u' w) \end{array}$
Although coarser than the Myhill equivalence, it is finite only if the latter is. Unlike the latter, it gives only a right congruence:
$u =_{N} u' implies u v =_{N} u' v$
and thus does not give rise to a semigroup. The number of equivalence classes is the number of states in the minimal machine for L.

单词	Nerode equivalence
释义	Nerode equivalence Computer An equivalence relation, =_N, arising in formal language theory. It is defined analogously to the Myhill equivalence by the weaker properties: $\begin{array}{l} for a language L over Σ, \\ u =_{N} u' \\ if, for all w in Σ^{}, \\ u w \in L iff u' w \in L \\ and for a function f, \\ u =_{N} u' \\ if, for all w in Σ^{}, \\ f (u w) = f (u' w) \end{array}$ Although coarser than the Myhill equivalence, it is finite only if the latter is. Unlike the latter, it gives only a right congruence: $u =_{N} u' implies u v =_{N} u' v$ and thus does not give rise to a semigroup. The number of equivalence classes is the number of states in the minimal machine for L.
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