Counting the answers to a query is a fundamental problem in databases, with several applications in the evaluation, optimization, and visualization of queries. Unfortunately, counting query answers is a #P-hard problem in most cases, so it is unlikely to be solvable in polynomial time. Recently, new results on approximate counting have been developed, specifically by showing that some problems in automata theory admit fully polynomial-time randomized approximation schemes. These results have several implications for the problem of counting the answers to a query; in particular, for graph and conjunctive queries. In this work, we present the main ideas of these approximation results, by using labeled DAGs instead of automata to simplify the presentation. In addition, we review how to apply these results to count query answers in different areas of databases.

计算查询的答案是数据库中的一个基本问题，在查询的评估、优化和可视化方面有多种应用。不幸的是，在大多数情况下，对查询答案进行计数是一个#P-hard 问题，因此它不太可能在多项式时间内得到解决。最近，关于近似计数的新结果已经得到发展，特别是通过表明自动机理论中的一些问题允许完全多项式时间随机近似方案。这些结果对计算查询答案的问题有几个影响；特别是对于图形和联合查询。在这项工作中，我们通过使用带标签的 DAG 而不是自动机来简化演示，展示了这些近似结果的主要思想。此外，