2024/10/14 by Filippo Bonchi, Elena Di Lavore, Bonchi, Filippo +3 · 1 voice · 1 citation
Computer Science · Mathematics · #18M35 #Category Theory (math.CT) #FOS: Computer and information sciences #FOS: Mathematics #Logic in Computer Science (cs.LO) #cs.LO #math.CT
paper · pdf · doi:10.48550/arxiv.2410.10627
arxiv published 2024/10/14 · arxiv updated 2026/06/25
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.