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.
Chapter PDF
Similar content being viewed by others
References
Saunders-Evans, L., Winskel, G.: Event structure spans for nondeterministic dataflow. Electr. Notes Theor. Comput. Sci. 175(3), 109–129 (2007)
Hyland, M.: Some reasons for generalising domain theory. Mathematical Structures in Computer Science 20(2), 239–265 (2010)
Cattani, G.L., Winskel, G.: Profunctors, open maps and bisimulation. Mathematical Structures in Computer Science 15(3), 553–614 (2005)
Abramsky, S., Melliès, P.A.: Concurrent games and full completeness. In: LICS 1999. IEEE Computer Society (1999)
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)
Conway, J.: On Numbers and Games. A K Peters, Wellesley (2000)
Joyal, A.: Remarques sur la théorie des jeux à deux personnes. Gazette des Sciences Mathématiques du Québec 1(4) (1997)
Winskel, G.: Event structures, stable families and games. Lecture notes, Comp. Science Dept. Aarhus University (2011), http://daimi.au.dk/~gwinskel
Rideau, S., Winskel, G.: Concurrent strategies. In: LICS 2011. IEEE Computer Society (2011)
Girard, J.Y.: The blind spot. European Mathematical Society (2011)
Hyland, M.: Game semantics. In: Pitts, A., Dybjer, P. (eds.) Semantics and Logics of Computation. Publications of the Newton Institute (1997)
Harmer, R., Hyland, M., Melliès, P.A.: Categorical combinatorics for innocent strategies. In: LICS 2007. IEEE Computer Society (2007)
Winskel, G.: Winning, losing and drawing in games with perfect and imperfect information. In: Festschrift for Dexter Kozen. LNCS. Springer, Heidelberg (2012)
Abramsky, S.: Semantics of interaction. In: Pitts, A., Dybjer, P. (eds.) Semantics and Logics of Computation. Publications of the Newton Institute (1997)
Winskel, G., Gutierrez, J., Clairambault, P.: The winning ways of concurrent games (2011) (in preparation)
Winskel, G.: Event structures with symmetry. Electr. Notes Theor. Comput. Sci. 172, 611–652 (2007)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights 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
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)