We introduce the resource calculus, a string diagrammatic language for concurrent systems. Significantly, it uses the same syntax and operational semantics as the signal flow calculus — an algebraic formalism for signal flow graphs, which is a combinatorial model of computation of interest in control theory. Indeed, our approach stems from the simple but fruitful realisation that, by replacing real numbers (modelling signals) with natural numbers (modelling resources) in the operational semantics, concurrent behaviour patterns emerge.
The resource calculus is canonical: we equip it and its stateful extension with equational theories that characterise the underlying space of definable behaviours—a convex algebraic universe of additive relations— via isomorphisms of categories. Finally, we demonstrate that our calculus is sufficiently expressive to capture behaviour definable by classical Petri nets.
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|Better Late Than Never: A Fully Abstract Semantics for Classical Processes
Wen Kokke University of Edinburgh, Fabrizio Montesi University of Southern Denmark, Marco Peressotti University of Southern DenmarkLink to publication DOI Media Attached
|Diagrammatic Algebra: From Linear to Concurrent Systems
Filippo Bonchi University of Pisa, Joshua Holland University of Southampton, Robin Piedeleu University of Oxford, Pawel Sobocinski University of Southampton, Fabio Zanasi University College LondonLink to publication DOI Media Attached
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Paolo Baldan University of Padova, Barbara König University of Duisburg-Essen, Christina Mika-Michalski University of Duisburg-Essen, Tommaso Padoan University of PadovaLink to publication DOI Media Attached File Attached