正则表达式提取上的聚合复杂度
The Complexity of Aggregates over Extractions by Regular Expressions
AI总结：
本文研究了在正则文档 spanner 之上应用 sum、average 等聚合函数查询文本的计算复杂度，证明了受限情况下可多项式时间精确计算，而一般情况精确计算难处理但部分聚合可通过 FPRAS 近似。
摘要：
带有捕获变量的正则表达式（也称为 regex-formulas）从文本中提取由其起始和结束索引标识的区间（spans）的关系。进而，正则文档 spanner 类是 regex formulas 在关系代数下的闭包。我们研究了在正则文档 spanner 之上通过聚合函数（如 sum、average 和 quantile）查询文本的计算复杂度。为此，我们正式定义了正则文档 spanner 上的聚合函数，并分析了精确计算与近似计算的计算复杂度。更准确地说，我们证明了在受限情况下，所有研究的聚合函数均可在多项式时间内计算。然而在一般情况下，尽管精确计算是难处理的，某些聚合函数仍可通过完全多项式时间随机近似方案（FPRAS）进行近似。
英文摘要：
Regular expressions with capture variables, also known as regex-formulas, extract relations of spans (intervals identified by their start and end indices) from text. In turn, the class of regular document spanners is the closure of the regex formulas under the Relational Algebra. We investigate the computational complexity of querying text by aggregate functions, such as sum, average, and quantile, on top of regular document spanners. To this end, we formally define aggregate functions over regular document spanners and analyze the computational complexity of exact and approximate computation. More precisely, we show that in a restricted case, all studied aggregate functions can be computed in polynomial time. In general, however, even though exact computation is intractable, some aggregates can still be approximated with fully polynomial-time randomized approximation schemes (FPRAS).
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