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- W4288336503 abstract "Turi and Plotkin's bialgebraic semantics is an abstract approach to specifying the operational semantics of a system, by means of a distributive law between its syntax (encoded as a monad) and its dynamics (an endofunctor). This setup is instrumental in showing that a semantic specification (a coalgebra) satisfies desirable properties: in particular, that it is compositional. In this work, we use the bialgebraic approach to derive well-behaved structural operational semantics of string diagrams, a graphical syntax that is increasingly used in the study of interacting systems across different disciplines. Our analysis relies on representing the two-dimensional operations underlying string diagrams in various categories as a monad, and their bialgebraic semantics in terms of a distributive law over that monad. As a proof of concept, we provide bialgebraic compositional semantics for a versatile string diagrammatic language which has been used to model both signal flow graphs (control theory) and Petri nets (concurrency theory). Moreover, our approach reveals a correspondence between two different interpretations of the Frobenius equations on string diagrams and two synchronisation mechanisms for processes, `a la Hoare and `a la Milner." @default.
- W4288336503 created "2022-07-29" @default.
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- W4288336503 date "2019-06-04" @default.
- W4288336503 modified "2023-09-24" @default.
- W4288336503 title "Bialgebraic Semantics for String Diagrams" @default.
- W4288336503 doi "https://doi.org/10.48550/arxiv.1906.01519" @default.
- W4288336503 hasPublicationYear "2019" @default.
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