论不奇补语的不歧义性
On the Power of Unambiguity in Büchi Complementation
摘要：
在这项工作中，我们利用\emph{unambiguity}的功能，Büchi自动机的互补问题，利用减少运行有向无环图（DAG）在无限的字，其中每个顶点最多有一个前任。然后，我们展示了如何使用这种类型的减少运行DAG作为一个\emph{unified tool}优化\emph{both}基于秩和切片的互补结构的Büchi自动机具有有限程度的模糊性。结果表明，给定一个具有$n$状态和有限模糊度的Büchi自动机，经典的基于秩和基于片的互补构造所构造的互补Büchi自动机的状态数可以分别从$2^{O(n\log n)}$改进为$2^{O(n)}$和从$O((3n)^n)$改进为$O(4^n)$.
英文摘要：
In this work, we exploit the power of \emph{unambiguity} for the complementation problem of Büchi automata by utilizing reduced run directed acyclic graphs (DAGs) over infinite words, in which each vertex has at most one predecessor. We then show how to use this type of reduced run DAGs as a \emph{unified tool} to optimize \emph{both} rank-based and slice-based complementation constructions for Büchi automata with a finite degree of ambiguity. As a result, given a Büchi automaton with $n$ states and a finite degree of ambiguity, the number of states in the complementary Büchi automaton constructed by the classical rank-based and slice-based complementation constructions can be improved, respectively, to $2^{O(n)}$ from $2^{O(n\log n)}$ and to $O(4^n)$ from $O((3n)^n)$.
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