An Interval Logic for Stream-Processing Functions: A Convolution-Based Construction

Abstract

We develop an interval-based logic for reasoning about systems consisting of components speci ed using stream-processing functions, which map streams of inputs to streams of outputs. The construction is algebraic and builds on a theory of convolution from formal power series. Using these algebraic foundations, we uniformly (and systematically) de ne operators for time- and space-based (de)composition. We also show that Banach's xed point theory can be incorporated into the framework, building on an existing theory of partially ordered monoids, which enables a feedback operator to be de ned algebraically.