This paper introduces process spaces, a unified theory of interacting systems. The main new trait, abstract executions, leads to a simple and general set formalism. For concurrent systems (including digital circuits), process spaces apply to diverse correctness concerns and yield a new classification of liveness and progress faults. The resulting studies of different correctness concerns are decoupled and homogeneous (i.e., they do not interfere with each other and they have the same algebraic structure). Applications to other interacting systems, such as electrical networks and dynamical systems, are also possible. Process spaces have many meaningful properties; here, some results from concurrency theory are generalized and simplified, and some new results are found.
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