域上的加权homo问题

IF 0.9 3区计算机科学 Q1 BUSINESS, FINANCE

Journal of Computer and System Sciences Pub Date : 2024-12-11 DOI:10.1016/j.jcss.2024.103616

Andreea-Teodora Nász

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引用次数: 0

摘要

已知hm问题是可判定的，它问的是在树同态下的正则树语言的象是否也是正则的。本文证明了在树同态是无俄罗斯方块（一个推广注入性的条件）的条件下，所有域都是可判定的加权hm -问题。为此，我们将问题简化为表示所讨论的同态象的器件的一个属性；为了证明这个性质是可判定的，我们从著名的由Berstel和Reutenauer在1982年证明的域上正则树级数的抽运引理中推导出这些装置的抽运引理。

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The weighted HOM-problem over fields

The HOM-problem, which asks whether the image of a regular tree language under a tree homomorphism is again regular, is known to be decidable. In this paper, we prove the weighted HOM-problem for all fields decidable, provided that the tree homomorphism is tetris-free (a condition that generalizes injectivity). To this end, we reduce the problem to a property of the device representing the homomorphic image in question; to prove this property decidable, we then derive a pumping lemma for such devices from the well-known pumping lemma for regular tree series over fields, proved by Berstel and Reutenauer in 1982.

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来源期刊

Journal of Computer and System Sciences 工程技术-计算机：理论方法

CiteScore

3.70

自引率

0.00%

发文量

审稿时长

68 days

期刊介绍： The Journal of Computer and System Sciences publishes original research papers in computer science and related subjects in system science, with attention to the relevant mathematical theory. Applications-oriented papers may also be accepted and they are expected to contain deep analytic evaluation of the proposed solutions. Research areas include traditional subjects such as: • Theory of algorithms and computability • Formal languages • Automata theory Contemporary subjects such as: • Complexity theory • Algorithmic Complexity • Parallel & distributed computing • Computer networks • Neural networks • Computational learning theory • Database theory & practice • Computer modeling of complex systems • Security and Privacy.