arXiv 0806.16022008-06-16cs.CGcs.LO

元胞自动机的整体函数在双曲平面上的内射性是不可判定的

The injectivity of the global function of a cellular automaton in the hyperbolic plane is undecidable

Margenstern Maurice

备注：: 9 figures this paper completely solves the problem tackled in arXiv:0712.2577v2. This version is simply an improvement of the proof of the result deposited in 0806.1602
发表信息：: The Injectivity of the Global Function of a Cellular Automaton in the Hyperbolic Plane is Undecidable, Fundamenta Informaticae, 94(1), (2009), 63-99

摘要：

在本文中，我们研究以下问题。我们考虑在双曲平面上的细胞自动机，我们考虑在所有可能的配置上定义的全局函数。这个函数的内射性是不可判定的吗？这个问题在1994年由Jarkko Kari在欧几里得平面的情况下得到了积极的回答。在本文中，我们表明，答案也是积极的双曲平面：问题是不可判定的。

英文摘要：

In this paper, we look at the following question. We consider cellular automata in the hyperbolic plane and we consider the global function defined on all possible configurations. Is the injectivity of this function undecidable? The problem was answered positively in the case of the Euclidean plane by Jarkko Kari, in 1994. In the present paper, we show that the answer is also positive for the hyperbolic plane: the problem is undecidable.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。