有界度结构上的一阶查询是具有常数延迟的可计算查询
First-order queries on structures of bounded degree are computable with constant delay
摘要：
一个有界度结构要么是一个所有关系都有界度的关系结构，要么是一个只包含双射函数的函数结构。在本文中，我们重新评估问题的复杂性不一定布尔一阶查询有界度的结构。查询评估在这里被认为是一个动态的过程。我们证明了有界度结构上的任何查询都是$\constantdelaylin$，即，可以通过具有两个单独部分的算法来计算：它具有结构大小的线性时间的预计算步骤，然后，它逐个输出所有元组，每个元组之间具有常数（即仅取决于公式的大小）延迟。作为一个全局过程，这意味着对有界结构的查询可以在总时间$O(f(|ϕ|).(|\calS|+|ϕ(\calS)|))$和总空间$O(f(|ϕ|).|\calS|)$中进行计算，其中$\calS$是结构，$ϕ$是公式，$ϕ(\calS)$是查询结果，$f$是某个函数。除其他事项外，我们的结果推广了\cite{Seese-96}的数据复杂性的有界度结构的模型检测问题的结果。此外，我们的方法相比，\cite{Seese-96}和可比的结果的独创性是，它不依赖于Hanf的模型理论技术（见\cite{Hanf-65}），是完全有效的。
英文摘要：
A bounded degree structure is either a relational structure all of whose relations are of bounded degree or a functional structure involving bijective functions only. In this paper, we revisit the complexity of the evaluation problem of not necessarily Boolean first-order queries over structures of bounded degree. Query evaluation is considered here as a dynamical process. We prove that any query on bounded degree structures is $\constantdelaylin$, i.e., can be computed by an algorithm that has two separate parts: it has a precomputation step of linear time in the size of the structure and then, it outputs all tuples one by one with a constant (i.e. depending on the size of the formula only) delay between each. Seen as a global process, this implies that queries on bounded structures can be evaluated in total time $O(f(|ϕ|).(|\calS|+|ϕ(\calS)|))$ and space $O(f(|ϕ|).|\calS|)$ where $\calS$ is the structure, $ϕ$ is the formula, $ϕ(\calS)$ is the result of the query and $f$ is some function. Among other things, our results generalize a result of \cite{Seese-96} on the data complexity of the model-checking problem for bounded degree structures. Besides, the originality of our approach compared to that \cite{Seese-96} and comparable results is that it does not rely on the Hanf's model-theoretic technic (see \cite{Hanf-65}) and is completely effective.
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