Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: 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 µ-calculus. The known upper bound is NP∩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  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.
['Jan Obdržálek']
I am writing a research paper on a idea Clique-width and parity games
[{"from": "human", "value": "I am writing a research paper on a idea Clique-width and parity games"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: 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 \u00b5-calculus. The known upper bound is NP\u2229co-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  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."}]