In reactive systems, execution is driven by external events to which the system should respond with appropriate actions. Such events can be simple, but systems are often supposed to react to sophisticated situations involving a number of simpel events occurring in accordance with some pattern. A systematic approach to handle this type of systems is to separate the mechanism for detecting composite events from the rest of the application logic. A detection mechanism listens for simple event occurrences and notifies the application when one of the complex event patterns of interest occur. The event detection mechanism can for example be based on an event algebra, i.e., expressions that correspond to the event patterns of interest are built from simple events and operators from the algebra.
This thesis presents a novel event algebra with two important characteristics: It complies with algebraic laws that intuitively ought to hold for the operators of the algebra, and for a large class of expressions the detection can be correctly performed with limited resources in terms of memory and time. In addition to the declarative algebra semantics, we present an imperative detection algorithm and show that it correctly implements the algebra. This algorithm is analysed with respect to memory requirements and execution time complexity. To increase the efficiency of the algebra, we also present a semantic-preserving transformation scheme by which many expressions can be transformed to meet criteria under which limited resource requirements are guaranteed. Finally, we present a prototype implementation that combines the algebra with the event system in Java.