Using recent developments in coalgebraic and monad-based semantics, we present a uniform study of various notions of machines, e.g. finite state machines, multi-stack machines, Turing machines, valence automata, and weighted automata. They are instances of Jacobs' notion of a T-automaton, where T is a monad. We show that the generic language semantics for T-automata correctly instantiates the usual language semantics for a number of known classes of machines/languages, including regular, context-free, recursively-enumerable and various subclasses of context free languages (e.g. deterministic and real-time ones). Moreover, our approach provides new generic techniques for studying the expressivity power of various machine-based models.

中文翻译：

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走向有效状态机的统一理论

使用近代数和基于单子语义的发展，我们对机器的各种概念进行了统一研究，例如有限状态机、多堆栈机、图灵机、价自动机和加权自动机。它们是 Jacobs 的 T 自动机概念的实例，其中 T 是单子。我们展示了 T-automata 的通用语言语义正确实例化了许多已知机器/语言类别的常用语言语义，包括常规、上下文无关、递归可枚举和上下文无关语言的各种子类（例如确定性和实数-时间的）。此外，我们的方法为研究各种基于机器的模型的表达能力提供了新的通用技术。