We focus on the computational complexity of regular simple path queries (RSPQs). We consider the following problem RSPQ(L) for a regular language L: given an edge-labeled digraph G and two nodes x and y, is there a simple path from x to y that forms a word belonging to L? We fully characterize the frontier between tractability and intractability for $\mathrm{\text{RSPQ}}(L)$. More precisely, we prove $\mathrm{\text{RSPQ}}(L)$ is either

,

-complete or

-complete depending on the language L. We also provide a simple characterization of the tractable fragment in terms of regular expressions. Finally, we also discuss the complexity of deciding whether a language L belongs to the fragment above. We consider several alternative representations of L: DFAs, NFAs or regular expressions, and prove that this problem is

-complete for the first representation and

-complete for the other two.

中文翻译：

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图上常规简单路径查询的三分法

我们关注常规简单路径查询（RSPQ）的计算复杂性。我们考虑普通语言L的以下问题RSPQ（L）：给定一个带有边标记的有向图G和两个节点x和y，是否存在从x到y的简单路径，形成属于L的单词？我们充分刻画了易处理性和难处理性之间的边界$\mathrm{\text{RSPQ}}（\mathrm{大号}）$。更确切地说，我们证明$\mathrm{\text{RSPQ}}（\mathrm{大号}）$ 或者是

，

-完成或

根据语言-complete大号。我们还根据正则表达式提供了易处理片段的简单特征。最后，我们还讨论了确定语言L是否属于上述片段的复杂性。我们考虑L的几种替代表示形式：DFA，NFA或正则表达式，并证明此问题是

-完成第一次表示

-完成另外两个。