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A Mathematical Game Semantics of Concurrency and Nondeterminism

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Theoretical Aspects of Computing - ICTAC 2015 (ICTAC 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9399))

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Abstract

Concurrent games as event structures form a partial order model of concurrency where concurrent behaviour is captured by nondeterministic concurrent strategies—a class of maps of event structures. Extended with winning conditions, the model is also able to give semantics to logics of various kinds. An interesting subclass of this game model is the one considering deterministic strategies only, where the induced model of strategies can be fully characterised by closure operators. The model based on closure operators exposes many interesting mathematical properties and allows one to define connections with many other semantic models where closure operators are also used. However, such a closure operator semantics has not been investigated in the more general nondeterministic case. Here we do so, and show that some nondeterministic concurrent strategies can be characterised by a new definition of nondeterministic closure operators which agrees with the standard game model for event structures and with its extension with winning conditions.

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References

  1. Abramsky, S.: Sequentiality vs. concurrency in games and logic. Math. Struct. Comput. Sci. 13(4), 531–565 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  2. Abramsky, S., Jagadeesan, R., Malacaria, P.: Full abstraction for PCF. Inf. Comput. 163(2), 409–470 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  3. Abramsky, S., Melliès, P.: Concurrent games and full completeness. In: LICS, pp. 431–442. IEEE Computer Society (1999)

    Google Scholar 

  4. Berry, G.: Modèles complètement adéquats et stables des lambda-calculs typés. Ph.D. thesis, University of Paris VII (1979)

    Google Scholar 

  5. Clairambault, P., Gutierrez, J., Winskel, G.: The winning ways of concurrent games. In: LICS, pp. 235–244. IEEE Computer Society (2012)

    Google Scholar 

  6. Desel, J., Esparza, J.: ree Choice Petri Nets, Cambridge Tracts in Theoretical Computer Science, vol. 40. Cambridge University Press, Cambridge (1995)

    Book  MATH  Google Scholar 

  7. Gutierrez, J.: Concurrent logic games on partial orders. In: Beklemishev, L.D., de Queiroz, R. (eds.) WoLLIC 2011. LNCS, vol. 6642, pp. 146–160. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  8. Harmer, R., Hyland, M., Melliès, P.: Categorical combinatorics for innocent strategies. In: LICS, pp. 379–388. IEEE Computer Society (2007)

    Google Scholar 

  9. Hyland, J.M.E., Ong, C.L.: On full abstraction for PCF: I, II, and III. Inf. Comput. 163(2), 285–408 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  10. Kahn, G., Plotkin, G.: Concrete domains. Technical report, INRIA (1993)

    Google Scholar 

  11. Melliès, P.-A., Mimram, S.: Asynchronous games: innocence without alternation. In: Caires, L., Vasconcelos, V.T. (eds.) CONCUR 2007. LNCS, vol. 4703, pp. 395–411. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  12. Nielsen, M., Palamidessi, C., Valencia, F.D.: Temporal concurrent constraint programming: Denotation, logic and applications. Nord. J. Comput. 9(1), 145–188 (2002)

    MathSciNet  MATH  Google Scholar 

  13. Nielsen, M., Winskel, G.: Models for concurrency. In: Handbook of Logic in Computer Science, pp. 1–148. Oxford University Press (1995)

    Google Scholar 

  14. Olarte, C., Valencia, F.D.: Universal concurrent constraint programing: symbolic semantics and applications to security. In: SAC, pp. 145–150. ACM (2008)

    Google Scholar 

  15. Plotkin, G.D.: A powerdomain construction. SIAM J. Comput. 5(3), 452–487 (1976)

    Article  MathSciNet  MATH  Google Scholar 

  16. Rideau, S., Winskel, G.: Concurrent strategies. In: LICS, pp. 409–418. IEEE Computer Society (2011)

    Google Scholar 

  17. Saraswat, V.A., Rinard, M.C., Panangaden, P.: Semantic foundations of concurrent constraint programming. In: POPL, pp. 333–352. ACM Press (1991)

    Google Scholar 

  18. Saunders-Evans, L., Winskel, G.: Event structure spans for nondeterministic dataflow. Electron. Notes Theoret. Comput. Sci. 175(3), 109–129 (2007)

    Article  MATH  Google Scholar 

  19. Winskel, G.: Deterministic concurrent strategies. Formal Aspects Comput. 24(4–6), 647–660 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  20. Winskel, G.: Strategies as profunctors. In: Pfenning, F. (ed.) FOSSACS 2013 (ETAPS 2013). LNCS, vol. 7794, pp. 418–433. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

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Acknowledgment

I thank Paul Harrenstein, Glynn Winskel, and Michael Wooldridge for their comments and support. Also, I acknowledge with gratitude the support of the ERC Advanced Research Grant 291528 (“RACE”) at Oxford.

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Authors and Affiliations

  1. Department of Computer Science, University of Oxford, Oxford, UK

    Julian Gutierrez

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  1. Julian Gutierrez
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Correspondence to Julian Gutierrez .

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Editors and Affiliations

  1. University of LĂĽbeck, LĂĽbeck, Schleswig-Holstein, Germany

    Martin Leucker

  2. Pontificia Universidad Javeriana-Cali, Cali, Colombia

    Camilo Rueda

  3. Pontificia Universidad Javeriana-Cali, CNRS LIX École Polytechnique de Paris, Palaiseau Cedex, France

    Frank D. Valencia

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Gutierrez, J. (2015). A Mathematical Game Semantics of Concurrency and Nondeterminism. In: Leucker, M., Rueda, C., Valencia, F. (eds) Theoretical Aspects of Computing - ICTAC 2015. ICTAC 2015. Lecture Notes in Computer Science(), vol 9399. Springer, Cham. https://doi.org/10.1007/978-3-319-25150-9_35

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  • DOI: https://doi.org/10.1007/978-3-319-25150-9_35

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-25149-3

  • Online ISBN: 978-3-319-25150-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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