论文标题
针对连面查询工会的广义模型计数问题的二分法
A Dichotomy for the Generalized Model Counting Problem for Unions of Conjunctive Queries
论文作者
论文摘要
我们研究了$ gentrized〜模型〜计数问题$，定义如下：给定数据库和一组确定性元素，计算包含所有确定性元组并满足查询的数据库子集的数量。该问题在计算上等同于对元组概率数据库的查询评估，其中所有元素在$ \ {0，\ frac {1} {2}，1 \} $中具有概率。当概率是任意的有理数数字时，先前的工作已经建立了连接查询工会（UCQ）的二分法，这表明，对于每个查询，其复杂性在多项式时间或＃p-hard中。该查询在第一种情况下称为$ SAFE $，在第二种情况下$不安全$。在这里，我们通过证明不安全的UCQ查询仍然＃P-HARD来加强硬度证明，即使概率仅限于$ \ {0，\ frac {1} {2} {2}，1 \} $。这需要使用新技术的硬度证明进行完整的重新设计。一个相关的问题是$模型〜计数〜问题$，当输入概率仅限于$ \ {0，\ frac {1} {2} {2} \} $时，该问题要求查询的概率。尽管我们的结果并未扩展到所有不安全UCQ的模型计数，但我们证明，对于一类称为ITYPE-I禁止查询的不安全查询的模型计数是＃p-hard。
We study the $generalized~model~counting~problem$, defined as follows: given a database, and a set of deterministic tuples, count the number of subsets of the database that include all deterministic tuples and satisfy the query. This problem is computationally equivalent to the evaluation of the query over a tuple-independent probabilistic database where all tuples have probabilities in $\{0,\frac{1}{2},1\}$. Previous work has established a dichotomy for Unions of Conjunctive Queries (UCQ) when the probabilities are arbitrary rational numbers, showing that, for each query, its complexity is either in polynomial time or #P-hard. The query is called $safe$ in the first case, and $unsafe$ in the second case. Here, we strengthen the hardness proof, by proving that an unsafe UCQ query remains #P-hard even if the probabilities are restricted to $\{0,\frac{1}{2},1\}$. This requires a complete redesign of the hardness proof, using new techniques. A related problem is the $model~counting~problem$, which asks for the probability of the query when the input probabilities are restricted to $\{0,\frac{1}{2}\}$. While our result does not extend to model counting for all unsafe UCQs, we prove that model counting is #P-hard for a class of unsafe queries called Type-I forbidden queries.
