Petr nets, algebras, morphisms, and compositionality
Information and Computation
Theoretical Computer Science
Sequential and concurrent behaviour in Petri net theory
Theoretical Computer Science
Information and Computation
Theoretical Computer Science - Special volume on Petri nets
FoSSaCS '98 Proceedings of the First International Conference on Foundations of Software Science and Computation Structure
A Categorical Semantics of Quantum Protocols
LICS '04 Proceedings of the 19th Annual IEEE Symposium on Logic in Computer Science
Pure bigraphs: Structure and dynamics
Information and Computation
Abstract scalars, loops, and free traced and strongly compact closed categories
CALCO'05 Proceedings of the First international conference on Algebra and Coalgebra in Computer Science
Orthomodular Lattices in Occurrence Nets
PETRI NETS '09 Proceedings of the 30th International Conference on Applications and Theory of Petri Nets
The geometry and algebra of commitment
Ludics, dialogue and interaction
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We shall describe connections between Petri nets, quantum physics and category theory. The view of Net theory as a kind of discrete physics has been consistently emphasized by Carl-Adam Petri. The connections between Petri nets and monoidal categories were illuminated in pioneering work by Ugo Montanari and José Meseguer. Recent work by the author and Bob Coecke has shown how monoidal categories with certain additional structure (dagger compactness) can be used as the setting for an effective axiomatization of quantum mechanics, with striking applications to quantum information. This additional structure matches the extension of the Montanari-Meseguer approach by Marti-Oliet and Meseguer, motivated by linear logic.