Skip to main content

Advertisement

SpringerLink
Log in
Menu
Find a journal Publish with us
Search
Cart
Book cover

International Conference on Foundations of Software Science and Computational Structures

FoSSaCS 2012: Foundations of Software Science and Computational Structures pp 26–41Cite as

  1. Home
  2. Foundations of Software Science and Computational Structures
  3. Conference paper
Bicategories of Concurrent Games

Bicategories of Concurrent Games

(Invited Paper)

  • Glynn Winskel17 
  • Conference paper
  • 858 Accesses

  • 1 Citations

Part of the Lecture Notes in Computer Science book series (LNTCS,volume 7213)

Abstract

This paper summarises recent results on bicategories of concurrent games and strategies. Nondeterministic concurrent strategies, those nondeterministic plays of a game left essentially unchanged by composition with copy-cat strategies, have recently been characterized as certain maps of event structures. This leads to a bicategory of general concurrent games in which the maps are nondeterministic concurrent strategies. It is shown how the bicategory can be refined to a bicategory of winning strategies by adjoining winning conditions to games. Assigning “access levels” to moves addresses situations where Player or Opponent have imperfect information as to what has occurred in the game. Finally, a bicategory of deterministic “linear” strategies, a recently discovered model of MALL (multiplicative-additive linear logic), is described. All the bicategories become equivalent to simpler order-enriched categories when restricted to deterministic strategies.

Keywords

  • Games
  • strategies
  • concurrency
  • event structures
  • winning conditions
  • determinacy

Download conference paper PDF

References

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

    CrossRef  Google Scholar 

  2. Hyland, M.: Some reasons for generalising domain theory. Mathematical Structures in Computer Science 20(2), 239–265 (2010)

    CrossRef  MathSciNet  MATH  Google Scholar 

  3. Cattani, G.L., Winskel, G.: Profunctors, open maps and bisimulation. Mathematical Structures in Computer Science 15(3), 553–614 (2005)

    CrossRef  MathSciNet  MATH  Google Scholar 

  4. Abramsky, S., Melliès, P.A.: Concurrent games and full completeness. In: LICS 1999. IEEE Computer Society (1999)

    Google Scholar 

  5. 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)

    CrossRef  Google Scholar 

  6. Conway, J.: On Numbers and Games. A K Peters, Wellesley (2000)

    Google Scholar 

  7. Joyal, A.: Remarques sur la théorie des jeux à deux personnes. Gazette des Sciences Mathématiques du Québec 1(4) (1997)

    Google Scholar 

  8. Winskel, G.: Event structures, stable families and games. Lecture notes, Comp. Science Dept. Aarhus University (2011), http://daimi.au.dk/~gwinskel

  9. Rideau, S., Winskel, G.: Concurrent strategies. In: LICS 2011. IEEE Computer Society (2011)

    Google Scholar 

  10. Girard, J.Y.: The blind spot. European Mathematical Society (2011)

    Google Scholar 

  11. Hyland, M.: Game semantics. In: Pitts, A., Dybjer, P. (eds.) Semantics and Logics of Computation. Publications of the Newton Institute (1997)

    Google Scholar 

  12. Harmer, R., Hyland, M., Melliès, P.A.: Categorical combinatorics for innocent strategies. In: LICS 2007. IEEE Computer Society (2007)

    Google Scholar 

  13. Winskel, G.: Winning, losing and drawing in games with perfect and imperfect information. In: Festschrift for Dexter Kozen. LNCS. Springer, Heidelberg (2012)

    Google Scholar 

  14. Abramsky, S.: Semantics of interaction. In: Pitts, A., Dybjer, P. (eds.) Semantics and Logics of Computation. Publications of the Newton Institute (1997)

    Google Scholar 

  15. Winskel, G., Gutierrez, J., Clairambault, P.: The winning ways of concurrent games (2011) (in preparation)

    Google Scholar 

  16. Winskel, G.: Event structures with symmetry. Electr. Notes Theor. Comput. Sci. 172, 611–652 (2007)

    CrossRef  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Computer Laboratory, University of Cambridge, England

    Glynn Winskel

Authors
  1. Glynn Winskel
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. IT University of Copenhagen, Rued Langgaards Vej 7, 2300, Copenhagen, Denmark

    Lars Birkedal

Rights and permissions

Reprints and Permissions

Copyright information

© 2012 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Winskel, G. (2012). Bicategories of Concurrent Games. In: Birkedal, L. (eds) Foundations of Software Science and Computational Structures. FoSSaCS 2012. Lecture Notes in Computer Science, vol 7213. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28729-9_2

Download citation

  • .RIS
  • .ENW
  • .BIB
  • DOI: https://doi.org/10.1007/978-3-642-28729-9_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-28728-2

  • Online ISBN: 978-3-642-28729-9

  • eBook Packages: Computer ScienceComputer Science (R0)

Share this paper

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

Search

Navigation

  • Find a journal
  • Publish with us

Discover content

  • Journals A-Z
  • Books A-Z

Publish with us

  • Publish your research
  • Open access publishing

Products and services

  • Our products
  • Librarians
  • Societies
  • Partners and advertisers

Our imprints

  • Springer
  • Nature Portfolio
  • BMC
  • Palgrave Macmillan
  • Apress
  • Your US state privacy rights
  • Accessibility statement
  • Terms and conditions
  • Privacy policy
  • Help and support

167.114.118.210

Not affiliated

Springer Nature

© 2023 Springer Nature