Concurrent Games and Full Completeness
LICS '99 Proceedings of the 14th Annual IEEE Symposium on Logic in Computer Science
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Mathematical Structures in Computer Science
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Electronic Notes in Theoretical Computer Science (ENTCS)
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Electronic Notes in Theoretical Computer Science (ENTCS)
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LICS '07 Proceedings of the 22nd Annual IEEE Symposium on Logic in Computer Science
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Mathematical Structures in Computer Science
LICS '11 Proceedings of the 2011 IEEE 26th Annual Symposium on Logic in Computer Science
Winning, losing and drawing in concurrent games with perfect or imperfect information
Logic and Program Semantics
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CONCUR'07 Proceedings of the 18th international conference on Concurrency Theory
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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.