The chase procedure is a fundamental algorithmic tool in database theory with a variety of applications. A key problem concerning the chase procedure is all-instances termination: for a given set of tuple-generating dependencies (TGDs), is it the case that the chase terminates for every input database? In view of the fact that this problem is undecidable, it is natural to ask whether known well-behaved classes of TGDs, introduced in different contexts such as ontological reasoning, ensure decidability. We consider a prominent paradigm that led to a robust TGD-based formalism, called stickiness. We show that for sticky sets of TGDs, all-instances chase termination is decidable if we focus on the (semi-)oblivious chase, and we pinpoint its exact complexity: PSpace-complete in general, and NLogSpace-complete for predicates of bounded arity. These complexity results are obtained via a graph-based syntactic characterization of chase termination that is of independent interest.

跟踪过程是数据库理论中具有多种应用程序的基本算法工具。关于追逐程序的一个关键问题是全实例终止：对于给定的一组元组生成依赖项（TGD），追逐终止于每个输入数据库的情况是这样吗？鉴于这个问题是无法确定的，很自然地要问，在诸如本体论推理之类的不同上下文中引入的已知行为良好的TGD类是否能确保可确定性。我们认为一种显着的范式导致了基于TGD的稳健的形式主义，即粘性。我们表明，对于粘性的TGD集，如果我们关注（半）遗忘的追逐，则所有实例的追逐终止是可决定的，并且指出了其确切的复杂性：PSpace-总体上完整，NLogSpace-完成有限有条件谓词。这些复杂性结果是通过具有独立兴趣的追逐终止的基于图的句法表征获得的。