Abstract

Efficient processing of input data streams is central to IoT systems, and the goal of this paper is to develop a logical foundation for specifying the computation of such stream processing. In the proposed model, both the input and output of a stream processing system consists of tagged data items with a dependency relation over tags that captures the logical ordering constraints over data items. While a system processes the input data one item at a time, incrementally producing output data items, its semantics is a function from input data traces to output data traces, where a data trace is an equivalence class of sequences of data items induced by the dependency relation. This data-trace transduction model generalizes both acyclic Kahn process networks and relational query processors, and can specify computations over data streams with a rich variety of ordering and synchronization characteristics. To form complex systems from simpler ones, we define sequential composition and parallel composition operations over data-trace transductions, and show how to define commonly used idioms in stream processing such as sliding windows, key-based partitioning, and map-reduce.

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