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’s 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

利用代数和基于单子的语义的最新发展，我们对各种机器概念进行了统一研究，例如有限状态机、多栈机器、图灵机、价自动机和加权自动机。它们是 Jacobs 概念的实例吨-自动机， 在哪里吨是一个单子。我们证明了通用语言语义吨-automata 正确实例化了许多已知机器/语言类的常用语言语义，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，确定性和实时语言）。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。