We show how to compute efficiently with nominal sets over the total order symmetry, by developing a direct representation of such nominal sets and basic constructions thereon. In contrast to previous approaches, we work directly at the level of orbits, which allows for an accurate complexity analysis. The approach is implemented as the library ONS (Ordered Nominal Sets). Our main motivation is nominal automata, which are models for recognising languages over infinite alphabets. We evaluate ONS in two applications: minimisation of automata and active automata learning. In both cases, ONS is competitive compared to existing implementations and outperforms them for certain classes of inputs.

翻译：与以往的做法不同,我们直接在轨道一级工作,这样可以进行精确的复杂分析。我们采取的方法是作为ONS图书馆(ONS(Ordered Nominal Sets))实施。我们的主要动机是名义自动数据,这是识别无限字母语言的模型。我们用两种应用来评价ONS:最小化自动成像和主动自动成像学习。在这两种情况下,ONS与现有的实施相比具有竞争力,并且在某些输入类别中优于这些功能。