有界振荡语言的有理指数
Rational index of bounded-oscillation languages
摘要：
上下文无关语言$L$的有理索引是一个函数$f(n)$，使得对于由具有$n$状态的自动机识别的每个正则语言$R$，$L$和$R$的交集要么是空的，要么包含比$f(n)$短的词。已知上下文无关语言（CFL-）可达性问题和多项式有理索引上下文无关语言（查询）的数据库查询求值问题是NC问题，而这些问题在一般情况下是P-完全的.我们研究了有界振荡语言的有理指数，并证明了它是多项式阶的。我们得到了上界的合理指数的值一般有界振荡语言和一些以前研究的子类。
英文摘要：
The rational index of a context-free language $L$ is a function $f(n)$, such that for each regular language $R$ recognized by an automaton with $n$ states, the intersection of $L$ and $R$ is either empty or contains a word shorter than $f(n)$. It is known that the context-free language (CFL-)reachability problem and Datalog query evaluation for context-free languages (queries) with the polynomial rational index is in NC, while these problems is P-complete in the general case. We investigate the rational index of bounded-oscillation languages and show that it is of polynomial order. We obtain upper bounds on the values of the rational index for general bounded-oscillation languages and for some of its previously studied subclasses.
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