Abstract
In recent work, the author and others have studied compositional algebras of Petri nets. Here we consider mathematical aspects of the pure linking algebras that underly them. We characterise composition of nets without places as the composition of spans over appropriate categories of relations, and study the underlying algebraic structures.
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Abramsky, S., Coecke, B.: A categorical semantics of quantum protocols. In: Logic in Computer Science (LiCS 2004). IEEE Press (2004)
Arbab, F.: Reo: A channel-based coordination model for component composition. Math. Struct. Comp. Sci. 14(3), 1–38 (2004)
Bruni, R., Lanese, I., Montanari, U.: A basic algebra of stateless connectors. Theor. Comput. Sci. 366, 98–120 (2006)
Bruni, R., Melgratti, H., Montanari, U.: A connector algebra for P/T nets interactions. In: Katoen, J.-P., König, B. (eds.) CONCUR 2011. LNCS, vol. 6901, pp. 312–326. Springer, Heidelberg (2011)
Bruni, R., Melgratti, H.C., Montanari, U., Sobociński, P.: Connector algebras for C/E and P/T nets’ interactions. Log. Meth. Comput. Sci. (to appear, 2013)
Carboni, A., Walters, R.F.C.: Cartesian bicategories I. J. Pure Appl. Algebra 49, 11–32 (1987)
Coecke, B., Paquette, É.O., Pavlovic, D.: Classical and quantum structuralism. In: Semantical Techniques in Quantum Computation, pp. 29–69. Cambridge University Press (2009)
Dickson, L.E.: Finiteness of the odd perfect and primitive abundant numbers with n distinct prime factors. Amer. Journal Math. 35(4), 413–422 (1913)
Fiore, M.P., Campos, M.D.: The algebra of directed acyclic graphs. In: Coecke, B., Ong, L., Panangaden, P. (eds.) Computation, Logic, Games and Quantum Foundations. LNCS, vol. 7860, pp. 37–51. Springer, Heidelberg (2013)
Girard, J.-Y.: Linear logic. Theor. Comput. Sci. 50, 1–102 (1987)
Hughes, D.J.D.: Linking diagrams for free. arXiv:0805.1441v1 (2008)
Joyal, A., Street, R.: The geometry of tensor calculus, i. Adv. Math. 88, 55–112 (1991)
Kelly, G.M., Laplaza, M.L.: Coherence for compact closed categories. J. Pure Appl. Algebra 19, 193–213 (1980)
Kissinger, A.: Synthesising graphical theories. arxiv.org:1202.6079 (2012)
Kock, J.: Frobenius algebras and 2D topological quantum field theories. Cambridge University Press (2003)
Lack, S.: Composing PROPs. Theor. App. Categories 13(9), 147–163 (2004)
Mac Lane, S.: Categorical algebra. Bull. Amer. Math. Soc. 71, 40–106 (1965)
Selinger, P.: Dagger compact closed categories and completely positive maps. In: Quantum Programming Languages (QPL 2007). ENTCS, vol. 170, pp. 139–163 (2007)
Selinger, P.: A survey of graphical languages for monoidal categories. arXiv:0908.3347v1 (math.CT) (2009)
Sobociński, P.: Representations of petri net interactions. In: Gastin, P., Laroussinie, F. (eds.) CONCUR 2010. LNCS, vol. 6269, pp. 554–568. Springer, Heidelberg (2010)
Sobociński, P., Stephens, O.: Reachability via compositionality in Petri nets. arXiv:1303.1399v1 (2013)
Sobociński, P., Stephens, O.: Penrose: Putting compositionality to work for petri net reachability. In: Heckel, R., Milius, S. (eds.) CALCO 2013. LNCS, vol. 8089, pp. 346–352. Springer, Heidelberg (2013)
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Sobociński, P. (2013). Nets, Relations and Linking Diagrams. In: Heckel, R., Milius, S. (eds) Algebra and Coalgebra in Computer Science. CALCO 2013. Lecture Notes in Computer Science, vol 8089. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40206-7_21
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DOI: https://doi.org/10.1007/978-3-642-40206-7_21
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