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2273 Finally we like to show that the Myhill-Nerode Theorem is also convenient for establishing |
2273 Finally we like to show that the Myhill-Nerode Theorem is also convenient for establishing |
2274 the non-regularity of languages. For this we use the following version of the Continuation |
2274 the non-regularity of languages. For this we use the following version of the Continuation |
2275 Lemma (see for example~\cite{Rosenberg06}). |
2275 Lemma (see for example~\cite{Rosenberg06}). |
2276 |
2276 |
2277 \begin{lmm}[Continuation Lemma] |
2277 \begin{lmm}[Continuation Lemma] |
2278 If a language @{text A} is regular and a set @{text B} is infinite, |
2278 If a language @{text A} is regular and a set of strings @{text B} is infinite, |
2279 then there exist two distinct strings @{text x} and @{text y} in @{text B} |
2279 then there exist two distinct strings @{text x} and @{text y} in @{text B} |
2280 such that @{term "x \<approx>A y"}. |
2280 such that @{term "x \<approx>A y"}. |
2281 \end{lmm} |
2281 \end{lmm} |
2282 |
2282 |
2283 \noindent |
2283 \noindent |