We propose a method for solving parity games with acyclic (DAG) sub-structures by computing nested fixpoints of a DAG attractor function that lives over the non-DAG parts of the game, thereby restricting the domain of the involved fixpoint operators. Intuitively, this corresponds to accelerating fixpoint computation by inlining cycle-free parts during the solution of parity games, leading to earlier convergence. We also present an economic later-appearence-record construction that takes Emerson-Lei games to parity games, and show that it preserves DAG sub-structures; it follows that the proposed method can be used also for the accelerated solution of Emerson-Lei games.

翻译：我们提出一种方法，用于求解包含无环子结构（即DAG）的奇偶博弈。该方法通过计算一个定义在博弈非DAG部分上的DAG吸引子函数的嵌套不动点，从而限制所涉及不动点算子的定义域。直观上，这相当于在求解奇偶博弈时通过内联无环部分来加速不动点计算，从而实现更早的收敛。我们还提出一种经济型后出现记录构造，将Emerson-Lei博弈转化为奇偶博弈，并证明该构造能保持DAG子结构；由此可知，所提出的方法也可用于加速求解Emerson-Lei博弈。