论文标题
常规路径查询的语义树宽度和路径宽度
Semantic Tree-Width and Path-Width of Conjunctive Regular Path Queries
论文作者
论文摘要
我们表明，查询是否等同于对树宽度$ k $的查询的问题是可以决定的，对于带有双向导航（UC2RPQS）的连接常规路径查询类别的类别。 Barceló，Romero和Vardi的先前结果[Siam on Computing，2016年]显示了$ k = 1 $的案例的可决定性，在这里我们扩展了此结果，表明实际上可确定性为任何任意$ k \ geq 1 $。该算法位于2Expspace中，但是对于限制但实际上相关的情况，查询的所有正则表达式均为$ a^*$或$（a_1 + \ dotsb + a_n）$，我们表明问题的复杂性降至$π^p_2 $。 我们还通过小树宽度的查询研究了相关的问题的问题。我们展示了一种算法，该算法对于任何固定数字$ k $，都建立了UC2RPQ的树宽度$ k $的最大不足。查询$ q $的树宽度$ k $的最大不足是QUERY $ q'$ q'$ q $ q $ q $ q $以最大和独特的方式包含在$ q $中，也就是说，如果每个查询$ q'$ q'$ q'的$ q'$ q'$ q'$ q $ q $ q $ q $ q是$ q''in $ q'' 从某种意义上说，我们的方法也证明是可靠的，它还允许测试给定路径宽度的查询的等效性，它还涵盖了以前已知的结果$ k = 1 $，并且可以测试（单向）UCRPQ是否等于（单向）UCRPQ是否等于给定的树宽度的UCRPQ（或途径）。
We show that the problem of whether a query is equivalent to a query of tree-width $k$ is decidable, for the class of Unions of Conjunctive Regular Path Queries with two-way navigation (UC2RPQs). A previous result by Barceló, Romero, and Vardi [SIAM Journal on Computing, 2016] has shown decidability for the case $k=1$, and here we extend this result showing that decidability in fact holds for any arbitrary $k\geq 1$. The algorithm is in 2ExpSpace, but for the restricted but practically relevant case where all regular expressions of the query are of the form $a^*$ or $(a_1 + \dotsb + a_n)$ we show that the complexity of the problem drops to $Π^P_2$. We also investigate the related problem of approximating a UC2RPQ by queries of small tree-width. We exhibit an algorithm which, for any fixed number $k$, builds the maximal under-approximation of tree-width $k$ of a UC2RPQ. The maximal under-approximation of tree-width $k$ of a query $q$ is a query $q'$ of tree-width $k$ which is contained in $q$ in a maximal and unique way, that is, such that for every query $q''$ of tree-width $k$, if $q''$ is contained in $q$ then $q''$ is also contained in $q'$. Our approach is shown to be robust, in the sense that it allows also to test equivalence with queries of a given path-width, it also covers the previously known result for $k=1$, and it allows to test for equivalence of whether a (one-way) UCRPQ is equivalent to a UCRPQ of a given tree-width (or path-width).
