We present a unified translation of linear temporal logic (LTL) formulas into deterministic Rabin automata (DRA), limit-deterministic Büchi automata (LDBA), and nondeterministic Büchi automata (NBA). The translations yield automata of asymptotically optimal size (double or single exponential, respectively). All three translations are derived from one single Master Theorem of purely logical nature. The Master Theorem decomposes the language of a formula into a positive Boolean combination of languages that can be translated into ω-automata by elementary means. In particular, Safra’s, ranking, and breakpoint constructions used in other translations are not needed. We further give evidence that this theoretical clean and compositional approach does not lead to large automata per se and in fact in the case of DRAs yields significantly smaller automata compared to the previously known approach using determinisation of NBAs.

中文翻译：

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线性时序逻辑到 ω-Automata 的统一转换

我们将线性时序逻辑 (LTL) 公式统一转换为确定性拉宾自动机 (DRA)、极限确定性布奇自动机 (LDBA) 和非确定性布奇自动机 (NBA)。平移产生渐近最优大小的自动机（分别为双指数或单指数）。所有三种翻译都源自一个纯逻辑性质的主定理。主定理将公式的语言分解为可以通过基本手段翻译成 ω-自动机的语言的正布尔组合。特别是，不需要在其他翻译中使用的 Safra、排名和断点结构。