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The Structure of Concurrent Process Histories

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Coordination Models and Languages (COORDINATION 2021)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 12717))

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Abstract

We identify the algebraic structure of the material histories generated by concurrent processes. Specifically, we extend existing categorical theories of resource convertibility to capture concurrent interaction. Our formalism admits an intuitive graphical presentation via string diagrams for proarrow equipments.

This research was supported by the ESF funded Estonian IT Academy research measure (project 2014-2020.4.05.19-0001).

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References

  1. Abramsky, S.: What are the fundamental structures of concurrency? we still don’t know! CoRR abs/1401.4973 (2014)

    Google Scholar 

  2. Cockett, J.R.B., Pastro, C.: The logic of message-passing. Sci. Comput. Program. 74, 498–533 (2009)

    Article  MathSciNet  Google Scholar 

  3. Cockett, J.R.B., Seely, R.A.G.: Proof theory of the cut rule. In: Landry, E. (ed.) Categories for the Working Philosopher, pp. 223–261. Oxford University Press, Oxford (2017)

    Google Scholar 

  4. Coecke, B., Fritz, T., Spekkens, R.W.: A mathematical theory of resources. Inf. Comput. 250, 59–86 (2016)

    Article  MathSciNet  Google Scholar 

  5. Dawson, R., Paré, R.: What is a free double category like? J. Pure Appl. Algebra 168(1), 19–34 (2002)

    Article  MathSciNet  Google Scholar 

  6. Ehresmann, C.: Catágories structurées. Annales scientifiques de l’École Normale Supérieure 80(4), 349–426 (1963)

    Article  MathSciNet  Google Scholar 

  7. Fiore, M., Paoli, S., Pronk, D.: Model structures on the category of small double categories. Algebraic Geometric Topol. 8(4), 1855–1959 (2008)

    Article  MathSciNet  Google Scholar 

  8. Fong, B., Spivak, D.I.: Seven Sketches in Compositionality: An Invitation to Applied Category Theory (2018)

    Google Scholar 

  9. Grandis, M., Pare, R.: Adjoint for double categories. Cahiers de Topologie et Géométrie Différentielle Catégoriques 45(3), 193–240 (2004)

    MathSciNet  MATH  Google Scholar 

  10. Hoare, C.A.R.: Communicating sequential processes. Commun. ACM 21(8), 666–677 (1978)

    Article  Google Scholar 

  11. Myers, D.J.: String Diagrams For Double Categories and Equipments. arXiv e-prints (2016)

    Google Scholar 

  12. Joyal, A., Street, R.: The geometry of tensor calculus, I. Adv. Math. 88(1), 55–112 (1991)

    Article  MathSciNet  Google Scholar 

  13. Katis, P., Sabadini, N., Walters, R.F.C.: Span(Graph): a categorical algebra of transition systems. In: Johnson, M. (ed.) AMAST 1997. LNCS, vol. 1349, pp. 307–321. Springer, Heidelberg (1997). https://doi.org/10.1007/BFb0000479

    Chapter  Google Scholar 

  14. Mac Lane, S.: Categories for the Working Mathematician. Springer, New York (1971). https://doi.org/10.1007/978-1-4612-9839-7

    Book  MATH  Google Scholar 

  15. Meseguer, J., Montanari, U.: Petri nets are monoids. Inf. Comput. 88(2), 105–155 (1990)

    Article  MathSciNet  Google Scholar 

  16. Milner, R. (ed.): A Calculus of Communicating Systems. LNCS, vol. 92. Springer, Heidelberg (1980). https://doi.org/10.1007/3-540-10235-3

    Book  MATH  Google Scholar 

  17. Milner, R.: Communicating and Mobile Systems: The Pi-Calculus. Cambridge University Press, Cambridge (1999)

    MATH  Google Scholar 

  18. Petri, C.A.: Communication with automata (1966)

    Google Scholar 

  19. Selinger, P.: A survey of graphical languages for monoidal categories. In: New Structures for Physics, pp. 289–355. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-12821-9_4

  20. Shulman, M.: Framed bicategories and monoidal fibrations. Theory Appl. Categories 20(18), 650–738 (2008)

    MathSciNet  MATH  Google Scholar 

  21. Shulman, M.A.: Constructing symmetric monoidal bicategories. arXiv e-prints (2010)

    Google Scholar 

  22. Wood, R.J.: Abstract pro arrows I. Cahiers de Topologie et Géométrie Différentielle Catégoriques 23(3), 279–290 (1982)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Tallinn University of Technology, Tallinn, Estonia

    Chad Nester

Authors
  1. Chad Nester
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Editor information

Editors and Affiliations

  1. University of Turin, Turin, Italy

    Ferruccio Damiani

  2. Sir Alwyn William Building, University of Glasgow, Glasgow, UK

    Ornela Dardha

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Nester, C. (2021). The Structure of Concurrent Process Histories. In: Damiani, F., Dardha, O. (eds) Coordination Models and Languages. COORDINATION 2021. Lecture Notes in Computer Science(), vol 12717. Springer, Cham. https://doi.org/10.1007/978-3-030-78142-2_13

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  • DOI: https://doi.org/10.1007/978-3-030-78142-2_13

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-78141-5

  • Online ISBN: 978-3-030-78142-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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