This work studies Complex Event Recognition (CER) under time constraints regarding its query language, computational models, and streaming evaluation algorithms. We start by introducing an extension of Complex Event Logic (CEL), called timed CEL, with simple time operators. We show that timed CEL aids in modeling CER query languages in practice, serving as a proxy to study the expressive power of such languages under time constraints. For this purpose, we introduce an automata model for studying timed CEL, called timed Complex Event Automata (timed CEA). This model extends the existing CEA model with clocks, combining CEA and timed automata in a single model. We show that timed CEL and timed CEA are equally expressive, giving the first characterization of CER query languages under time constraints. Then, we move towards understanding the efficient evaluation of timed CEA over streams concerning its determinization and efficient algorithms. We present a class of timed CEA that are closed under determinization; furthermore, we show that this class contains swg-queries, an expressive class of CER queries recently introduced by Kleest-Meissner et al. Finally, we present a streaming evaluation algorithm with constant update time and output-linear delay for evaluating deterministic monotonic timed CEA with a single clock, which have only less equal or greater equal comparisons.

翻译：本研究针对时间约束下的复杂事件识别（CER），探讨其查询语言、计算模型及流式评估算法。我们首先引入一种扩展的复杂事件逻辑（CEL），称为时序CEL，该逻辑包含简单的时间运算符。研究表明，时序CEL有助于在实践中建模CER查询语言，可作为研究时间约束下此类语言表达能力的代理工具。为此，我们提出一种用于研究时序CEL的自动机模型，称为时序复杂事件自动机（时序CEA）。该模型通过引入时钟机制扩展了现有CEA模型，将CEA与时间自动机融合于统一框架中。我们证明时序CEL与时序CEA具有同等表达能力，首次实现了时间约束下CER查询语言的完整刻画。随后，我们转向研究时序CEA在数据流上的高效评估问题，重点关注其确定化方法与高效算法。我们提出一类在确定化操作下封闭的时序CEA；进一步证明该类包含swg-查询——这是Kleest-Meissner等人近期提出的具有强表达能力的CER查询类别。最后，我们提出一种具有恒定更新时间与输出线性延迟的流式评估算法，适用于评估仅含"小于等于"或"大于等于"比较运算的单时钟确定性单调时序CEA。