某些与词或树自动机相关的拓扑的 Polish 性质
逻辑
2023-06-22 v4 形式语言与自动机理论
计算机科学中的逻辑
摘要
我们证明了 B"uchi 拓扑和自动拓扑是 Polish 空间。我们还表明，这一结论不能完全推广到无限标记二叉树空间的情况；特别是，在这种情况下 B"uchi 拓扑和 Muller 拓扑不是 Polish 空间。
引用
@article{arxiv.1710.04002,
title = {Polishness of some topologies related to word or tree automata},
author = {Olivier Finkel and Olivier Carton and Dominique Lecomte},
journal= {arXiv preprint arXiv:1710.04002},
year = {2023}
}
备注
This paper is an extended version of a paper which appeared in the proceedings of the 26th EACSL Annual Conference on Computer Science and Logic, CSL 2017. The main addition with regard to the conference paper consists in the study of the B\"uchi topology and of the Muller topology in the case of a space of trees, which now forms Section 4