Publication details
Clique-Width and Parity Games
| Authors | |
|---|---|
| Year of publication | 2007 |
| Type | Article in Proceedings |
| Conference | Computer Science Logic 2007, proceedings |
| MU Faculty or unit | |
| Citation | |
| Field | Informatics |
| Keywords | parity games; mu-calculus; clique-width |
| Description | The question of the exact complexity of solving parity games is one of the major open problems in system verification, as it is equivalent to the problem of model-checking the modal $\mu$-calculus. The known upper bound is NP$\cap$co-NP, but no polynomial algorithm is known. It was shown that on tree-like graphs (of bounded tree-width and DAG-width) a polynomial-time algorithm does exist. Here we present a polynomial-time algorithm for parity games on graphs of bounded clique-width (class of graphs containing e.g. complete bipartite graphs and cliques), thus completing the picture. This also extends the tree-width result, as graphs of bounded tree-width are a subclass of graphs of bounded clique-width. The algorithm works in a different way to the tree-width case and relies heavily on an interesting structural property of parity games. |
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