Model-based design methods have become common practice for the design, analysis, and synthesis of embedded and cyber-physical systems. Different models of computation are used (for example state-based models, dataflow models, differential equations, hybrid-models). In real-time and cyber-physical systems it is common to incorporate in such models some representation of time, physical, logical or otherwise. We are used to time progressing in forward direction. This assumption is built into the very definition of many of our favorite models of computation. Execution times or delays are usually non-negative. Time stamps usually increase monotonically. Tasks can depend on past activations of other tasks, but not on future activations. Tasks are temporally causal. In this paper we explore the possibilities and the potential benefits of liberating our models from these assumptions, allowing time go backward in our models. We will use the dataflow model of computation for our exploration and show that there are potential benefits to negative execution times, negative delays on channels, and non-monotone events in event traces.
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