论分离词与分离反义词的差距
On the Gap Between Separating Words and Separating Their Reversals
摘要：
如果确定性有限自动机（DFA）接受$w$并拒绝$x$，则它会分离两个字符串$w$和$x$。DFA分离$w$和$x$所需的状态的最小数量由$sep(w,x)$表示。本文表明，差异$|sep(w,x)-sep(w^R,x^R)|$是无界的二进制字母表，这里$w^R$代表的镜像$w$。这解决了在[Demaine，Eisenstat，Shallit，Wilson：Remarks on separating words. DCFS 2011。LNCS vol. 6808，pp. 147-157.]
英文摘要：
A deterministic finite automaton (DFA) separates two strings $w$ and $x$ if it accepts $w$ and rejects $x$. The minimum number of states required for a DFA to separate $w$ and $x$ is denoted by $sep(w,x)$. The present paper shows that the difference $|sep(w,x)-sep(w^R,x^R)|$ is unbounded for a binary alphabet; here $w^R$ stands for the mirror image of $w$. This solves an open problem stated in [Demaine, Eisenstat, Shallit, Wilson: Remarks on separating words. DCFS 2011. LNCS vol. 6808, pp. 147-157.]
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