A formal query language and automata model for aggregation in complex event recognition

2026-01-02

arXiv.org

AI Summary

This work addresses the lack of formal semantic support for aggregation operations in existing complex event processing systems, where query languages offer only limited aggregation capabilities. To overcome this limitation, the paper proposes ACEL, the first complex event query language that supports arbitrary commutative monoid aggregations, and introduces a bag-based semantic model that enables unrestricted composition of aggregation and logical operators. Furthermore, the authors develop Aggregation Complex Event Automata (ACEA) as a computational model for ACEL and present a compilation mechanism translating ACEL queries into ACEA. Theoretical analysis demonstrates that ACEA strictly surpasses ACEL in expressive power, thereby establishing a rigorous formal foundation for aggregation-aware querying in complex event processing.

Technology Category

• Data Mining & Knowledge Management: Intelligent Query Processing
• Cognitive Modeling & Cognitive Systems: Agent Architectures
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning

Application Category

• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• Graph Algorithms and Modeling for the Web: Querying, indexing, and retrieval in Web-related graphs
• Search and Retrieval-Augmented AI: Agentic search

Abstract

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.

Problem

• Complex Event Recognition
• aggregation
• query language
• formal semantics
• event streams

Innovation

• aggregation
• complex event recognition
• formal query language
• automata model
• commutative monoid