有限自动机歧义度的更强界
Stronger bounds on the degree of ambiguity of finite automata
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中文总结 AI 辅助
本文研究非确定性有限自动机的歧义度，将Weber和Seidl的指数上界从$2^{O(n \n)}$改进为渐近紧的$2^{O(n)}$。
中文摘要 AI 辅助
歧义度衡量非确定性有限自动机（NFA）中接受运行的数量。我们考虑有限歧义的NFA，即存在一个常数$N$，使得对于每个单词$w$，至多有$N$个接受运行。在这种情况下，我们也称该NFA是$N$-歧义的。重要的是，$N$仅依赖于NFA本身，而不依赖于单词的长度。Weber和Seidl证明了每个NFA对于$N = 2^{O(n \n)}$是$N$-歧义的，其中$n$是状态数。我们将此改进为$N = 2^{O(n)}$，这在渐近意义上是紧的。
英文摘要
Ambiguity measures the number of accepting runs in nondeterministic finite automata (NFA). We consider finitely ambiguous NFA, where there exists a constant $N$ such that over every word $w$ there are at most $N$ accepting runs. In such a case we also say that the NFA is $N$-ambiguous. Importantly $N$ depends only on the NFA, it does not depend on the length of the word. Weber and Seidl showed that every NFA is $N$-ambiguous for $N = 2^{O(n \log n)}$, where $n$ is the number of states. We improve this to $N = 2^{O(n)}$, which is asymptotically tight.
发表机构
- University of Oxford（牛津大学）
- University of Warsaw（华沙大学）
机构由 AI 辅助整理，请以论文原文为准。
