$\mu $-bicomplete categories and parity games

Luigi Santocanale

Displaying similar documents to “ $μ$ -bicomplete categories and parity games”

The alternation hierarchy for the theory of $μ$ -lattices.

Santocanale, Luigi (2001)

Theory and Applications of Categories [electronic only]

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Polarized category theory, modules, and game semantics.

Cockett, J.R.B., Seely, R.A.G. (2007)

Theory and Applications of Categories [electronic only]

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Fixpoints, games and the difference hierarchy

Julian C. Bradfield (2003)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

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Drawing on an analogy with temporal fixpoint logic, we relate the arithmetic fixpoint definable sets to the winning positions of certain games, namely games whose winning conditions lie in the difference hierarchy over $Σ_{2}^{0}$ . This both provides a simple characterization of the fixpoint hierarchy, and refines existing results on the power of the game quantifier in descriptive set theory. We raise the problem of transfinite fixpoint hierarchies.

Permissive strategies : from parity games to safety games

Julien Bernet, David Janin, Igor Walukiewicz (2002)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

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It is proposed to compare strategies in a parity game by comparing the sets of behaviours they allow. For such a game, there may be no winning strategy that encompasses all the behaviours of all winning strategies. It is shown, however, that there always exists a permissive strategy that encompasses all the behaviours of all memoryless strategies. An algorithm for finding such a permissive strategy is presented. Its complexity matches currently known upper bounds for the simpler problem...