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The optimal value computation for turned-based stochastic games withreachability objectives, also known as simple stochastic games, is one of thefew problems in $NP \cap coNP$ which are not known to be in $P$. However, thereare some cases where these games can be easily solved, as for instance when theunderlying graph is acyclic. In this work, we try to extend this tractabilityto several classes of games that can be thought as "almost" acyclic. We givesome fixed-parameter tractable or polynomial algorithms in terms of differentparameters such as the number of cycles or the size of the minimal feedbackvertex set.

Finding Optimal Strategies of Almost Acyclic Simple Stochatic Games