Complex Event Recognition (CER) systems are used to identify complex patterns in event streams, such as those found in stock markets, sensor networks, and other similar applications. An important task in such patterns is aggregation, which involves summarizing a set of values into a single value using an algebraic function, such as the maximum, sum, or average, among others. Despite the relevance of this task, query languages in CER typically support aggregation in a restricted syntactic form, and their semantics are generally undefined. In this work, we present a first step toward formalizing a query language with aggregation for CER. We propose to extend Complex Event Logic (CEL), a formal query language for CER, with aggregation operations. This task requires revisiting the semantics of CEL, using a new semantics based on bags of tuples instead of sets of positions. Then, we present an extension of CEL, called Aggregation CEL (ACEL), which introduces an aggregation operator for any commutative monoid operation. The operator can be freely composed with previous CEL operators, allowing users to define complex queries and patterns. We showcase several queries in practice where ACEL proves to be natural for specifying them. From the computational side, we present a novel automata model, called Aggregation Complex Event Automata (ACEA), that extends the previous proposal of Complex Event Automata (CEA) with aggregation and filtering features. Moreover, we demonstrate that every query in ACEL can be expressed in ACEA, illustrating the effectiveness of our computational model. Finally, we study the expressiveness of ACEA through the lens of ACEL, showing that the automata model is more expressive than ACEL.

翻译：复杂事件识别（CER）系统用于识别事件流中的复杂模式，例如在股票市场、传感器网络及其他类似应用中发现的事件模式。在此类模式中，一项重要任务是聚合，即通过代数函数（如最大值、求和或平均值等）将一组值汇总为单个值。尽管该任务具有重要性，但CER中的查询语言通常仅以受限的句法形式支持聚合，且其语义通常未明确定义。在本工作中，我们朝着形式化CER聚合查询语言迈出了第一步。我们提出扩展复杂事件逻辑（CEL）——一种用于CER的形式化查询语言，为其增加聚合操作。此任务需要基于元组包（而非位置集合）的新语义来重新审视CEL的语义。随后，我们提出一种称为聚合CEL（ACEL）的CEL扩展，该扩展为任何可交换幺半群运算引入了聚合运算符。该运算符可与现有的CEL运算符自由组合，使用户能够定义复杂的查询和模式。我们展示了多个实际查询案例，其中ACEL被证明能自然地描述这些查询。在计算层面，我们提出一种称为聚合复杂事件自动机（ACEA）的新型自动机模型，该模型通过聚合与过滤功能扩展了先前提出的复杂事件自动机（CEA）。此外，我们证明了每个ACEL查询均可在ACEA中表达，从而验证了我们计算模型的有效性。最后，我们通过ACEL的视角研究了ACEA的表达能力，表明该自动机模型比ACEL具有更强的表达能力。