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FSTTCS
2008
Springer

Graph Games on Ordinals

13 years 4 months ago
Graph Games on Ordinals
We consider an extension of Church’s synthesis problem to ordinals by adding limit transitions to graph games. We consider game arenas where these limit transitions are defined using the sets of cofinal states. In a previous paper, we have shown that such games of ordinal length are determined and that the winner problem is PSPACE-complete, for a subclass of arenas where the length of plays is always smaller than ωω. However, the proof uses a rather involved reduction to classical Muller games, and the resulting strategies need infinite memory. We adapt the LAR reduction to prove the determinacy in the general case, and to generate strategies with finite memory, using a reduction to games where the limit transitions are defined by priorities. We provide an algorithm for computing the winning regions of both players in these games, with a complexity similar to parity games. Its analysis yields three results: determinacy without hypothesis on the length of the plays, existence ...
Julien Cristau, Florian Horn
Added 09 Nov 2010
Updated 09 Nov 2010
Type Conference
Year 2008
Where FSTTCS
Authors Julien Cristau, Florian Horn
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