Open parity games are proposed as a compositional extension of parity games with algebraic operations, forming string diagrams of parity games. A potential application of string diagrams of parity games is to describe a large parity game with a given compositional structure and solve it efficiently as a divide-and-conquer algorithm by exploiting its compositional structure. Building on our recent progress in open Markov decision processes, we introduce Pareto fronts of open parity games, offering a framework for multi-objective solutions. We establish the positional determinacy of open parity games with respect to their Pareto fronts through a novel translation method. Our translation converts an open parity game into a parity game tailored to a given single-objective. Furthermore, we present a simple algorithm for solving open parity games, derived from this translation that allows the application of existing efficient algorithms for parity games. Expanding on this foundation, we develop a compositional algorithm for string diagrams of parity games.

翻译：开放奇偶博弈被提出作为奇偶博弈的一种组合扩展，其具有代数运算，形成奇偶博弈的弦图。奇偶博弈弦图的一个潜在应用是描述一个具有给定组合结构的大型奇偶博弈，并通过利用其组合结构，以分治算法高效地求解它。基于我们在开放马尔可夫决策过程方面的最新进展，我们引入了开放奇偶博弈的帕累托前沿，为多目标求解提供了一个框架。我们通过一种新颖的转换方法，确立了开放奇偶博弈关于其帕累托前沿的位置确定性。我们的转换方法将开放奇偶博弈转化为针对给定单目标定制的奇偶博弈。此外，我们提出了一种求解开放奇偶博弈的简单算法，该算法源自这种转换，从而允许应用现有的高效奇偶博弈求解算法。在此基础上，我们进一步为奇偶博弈弦图开发了一种组合算法。