Closure Properties of Locally Finite Omega Languages

An absolute characterisation of locally determined omega-colimits

Characterising colimiting omega-cocones of projection pairs in terms of least upper bounds of their embeddings and projections is important to the solution of recursive domain equations. We present a universal characterisation of this local property as omega-cocontinuity of locally continuous functors. We present a straightforward proof using the enriched Yoneda embedding. The proof can be generalised to Cattani and Fiore's notion of locality for adjoint pairs.

A decidable class of (nominal) omega-regular languages over an infinite alphabet

We define a class of languages of infinite words over infinite alphabets, and the corresponding automata. The automata used for recognition are a generalisation of deterministic Muller automata to the setting of nominal sets. Remarkably, the obtained languages are determined by their ultimately periodic fragments, as in the classical case. Closure under complement, union and intersection, and decidability of emptiness and equivalence are preserved by the generalisation. This is shown by using finite representations of the (otherwise infinite-state) defined class of automata.

基于状态的系统中递归的极限

The Limit of Recursion in State-based Systems

本文证明了ω^2严格界定模态可定义函数在可数结构上达到不动点所需的迭代次数，纠正并扩展了先前关于无交替μ-演算闭包序数的结论，通过引入保守良注释理论实现了直接且清晰的泵过程。

模态μ演算的空间逻辑与缠结算子

Spatial logic of modal mu-calculus and tangled closure operators

该研究将McKinsey和Tarski的拓扑模态逻辑成果拓展至模态μ演算与缠结算子逻辑，证明二者在拓扑空间上表达力等价，建立了相关逻辑的有限模型性质，拓展了剖分引理，得到多种语言在自稠密度量空间上的完备性与可靠性结果。