Fatal Attractors in Parity Games [chapter]

Michael Huth, Jim Huan-Pu Kuo, Nir Piterman
2013 Lecture Notes in Computer Science  
We study a new form of attractor in parity games and use it to define solvers that run in PTIME and are partial in that they do not solve all games completely. Technically, for color c this new attractor determines whether player c%2 can reach a set of nodes X of color c whilst avoiding any nodes of color less than c. Such an attractor is fatal if player c%2 can attract all nodes in X back to X in this manner. Our partial solvers detect fixed-points of nodes based on fatal attractors and
more » ... ly classify such nodes as won by player c%2. Experimental results show that our partial solvers completely solve benchmarks that were constructed to challenge existing full solvers. Our partial solvers also have encouraging run times in practice. For one partial solver we prove that its runtime is in O(| V | 3 ), that its output game is independent of the order in which attractors are computed, and that it solves all Büchi games.
doi:10.1007/978-3-642-37075-5_3 fatcat:uxqp357lvjb7pi5jv7e552hg24