发表机构
Department of Algebra and Geometry, Institute of Mathematics, Budapest University of Technology and Economics（布达佩斯技术与经济大学数学研究所代数与几何系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究预序半环中近似几何序列的完备化，证明其可等价于几何序列，并推广渐近预序刻画，应用于复合马尔可夫假设下二元假设检验的强逆指数。
AI 中文摘要
预序半环的研究受到计算机科学、图论和信息论中应用的推动，并为理解渐近预序提供了工具，该预序比较一对元素的大幂次。本文研究那些行为近似于幂序列、但未必等价于几何序列的序列。我们的主要结果是，预序半环允许完备化，使得这些我们称为近似几何的序列在完备化中变得等价于几何序列，并且现有的渐近预序刻画可推广到该完备化。我们提供了张量半环和图半环中若干类近似几何序列的例子。作为一个具体应用，我们确定了具有复合马尔可夫假设的二元假设检验的强逆指数。
英文摘要
The study of preordered semirings is motivated by applications in computer science, graph theory, and information theory, and provides tools for understanding the asymptotic preorder, which compares large powers of a pair of elements. This paper studies sequences which behave approximately as sequences of powers, but are not necessarily equivalent to geometric sequences. Our main result is that preordered semirings admit completions where such sequences, that we call approximately geometric, become equivalent to geometric sequences, and that existing characterizations of the asymptotic preorder extend to the completion. We provide several classes of examples of approximately geometric sequences in the semiring of tensors, and in the semiring of graphs. As a concrete application, we determine the strong converse exponent for binary hypothesis testing with composite Markov hypotheses.
Comments58 pages
