单计数器网的参数化普适性问题
Parametrized Universality Problems for One-Counter Nets
摘要：
我们研究了单计数器网络的语言通用性问题，也称为1维向量加法系统与状态（1-VASS），参数化的初始计数器值，或在运行过程中允许的计数器值的上限。OCN接受的语言（通过达到最终控制状态来定义）在两个参数中都是单调的。这就产生了两个自然的问题：1）是否存在一个初始的计数器值，使语言的普遍性？2)是否存在一个足够高的天花板，使有界语言是普遍的？虽然普通的普遍性问题是可判定的（和阿克曼完全），这些参数化的问题似乎减少到检查基本的结构属性的基本自动机，我们表明，事实上这两个问题是不可判定的。我们还研究了几个可判定子类的问题的复杂性，即明确的，确定性的系统，并为那些在一个单字母表。
英文摘要：
We study the language universality problem for One-Counter Nets, also known as 1-dimensional Vector Addition Systems with States (1-VASS), parameterized either with an initial counter value, or with an upper bound on the allowed counter value during runs. The language accepted by an OCN (defined by reaching a final control state) is monotone in both parameters. This yields two natural questions: 1) Does there exist an initial counter value that makes the language universal? 2) Does there exist a sufficiently high ceiling so that the bounded language is universal? Although the ordinary universality problem is decidable (and Ackermann-complete) and these parameterized problems seem to reduce to checking basic structural properties of the underlying automaton, we show that in fact both problems are undecidable. We also look into the complexities of the problems for several decidable subclasses, namely for unambiguous, and deterministic systems, and for those over a single-letter alphabet.
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。
