Behaviours of stateful monoidal processes are equivalence classes of compatible finite observations in discard bicategories, yielding functorial feedback semantics and a categorified compactness theorem for closed relations.
Effectful Mealy Machines
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abstract
Effectful Mealy machines, which we introduce, are a generalization of Mealy machines with global effects determined by an effectful triple. We provide semantics of effectful Mealy machines in terms of both bisimilarity and traces: bisimilarity is characterized syntactically, via uniform feedback; traces are constructed coinductively in terms of streams. We prove that this framework characterizes standard causal processes and existing flavours of Mealy machine, bisimilarity, and trace equivalence. In the commutative case, we introduce a monoidal generalization of Raney's causal functions: monoidal causal processes.
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Finite Observations, Infinite Behaviour: bicategorical semantics for stateful monoidal processes
Behaviours of stateful monoidal processes are equivalence classes of compatible finite observations in discard bicategories, yielding functorial feedback semantics and a categorified compactness theorem for closed relations.