关于通知上下文无关语言的Yamakami问题的一个解决方案
A Solution to Yamakami's Problem on Advised Context-free Languages
摘要：
Yamakami [2011，Theoret. Sci.]研究具有建议功能的上下文无关语言。这里，建议的长度被假定为与输入的长度相同。让CFL和CFL/n分别表示所有上下文无关语言和具有通知功能的语言的类。我们让CFL（2）表示两个上下文无关语言的交集类。一个有趣的研究方向是问CFL（2）相对于CFL有多复杂。Yamakami提出了CFL（2）- CFL/n中是否存在CFL免疫集的问题。到目前为止最著名的是LSPACE-CFL/n有一个CFL免疫集，其中LSPACE表示在语义空间中识别的语言类。我们对他的问题提出了一个肯定的解决办法。我们证明的两个关键概念是嵌套回文和Yamakami交换引理。交换引理适用于泵浦引理（Bar-Hillel引理）不起作用的情况。我们的证明是一个例子，显示如何有用的交换引理。
英文摘要：
Yamakami [2011, Theoret. Comput. Sci.] studies context-free languages with advice functions. Here, the length of an advice is assumed to be the same as that of an input. Let CFL and CFL/n denote the class of all context-free languages and that with advice functions, respectively. We let CFL(2) denote the class of intersections of two context-free languages. An interesting direction of a research is asking how complex CFL(2) is, relative to CFL. Yamakami raised a problem whether there is a CFL-immune set in CFL(2) - CFL/n. The best known so far is that LSPACE - CFL/n has a CFL-immune set, where LSPACE denotes the class of languages recognized in logarithmic-space. We present an affirmative solution to his problem. Two key concepts of our proof are the nested palindrome and Yamakami's swapping lemma. The swapping lemma is applicable to the setting where the pumping lemma (Bar-Hillel's lemma) does not work. Our proof is an example showing how useful the swapping lemma is.
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