一种用于有限自动机消歧的简单算法框架
A simple algorithmic framework for disambiguation of finite automata
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中文总结 AI 辅助
研究有限自动机消歧任务，提出一种简单算法框架，推广确定化子集构造，有保留原无歧义自动机、即时计算后继状态、多项式时间计算新状态等属性，还能用于部分消歧并可扩展到其他自动机模型。
中文摘要 AI 辅助
我们研究有限状态自动机的消歧任务，即将自动机转换为等价的无歧义自动机。通过开发一种新颖且简单的算法框架来实现，该框架推广了确定化的子集构造，具有一些理想属性：若原自动机无歧义则保留；能即时计算后继状态；以多项式时间计算每个新状态。还展示了如何将此框架用于部分消歧，通过改变构建新状态的标准开发了针对不同歧义级别的算法，这些算法也满足相应级别的条件，最后表明该消歧框架可轻松扩展到加权自动机等其他自动机模型。
英文摘要
We study the task of disambiguation of finite state automata, namely, converting an automaton into an equivalent, unambiguous one. We do this by developing a novel and simple algorithmic framework that generalizes the subset construction for determinization, and that satisfies some desirable properties: (1) it preserves the original automaton if it was already unambiguous, (2) it computes the successor states on-the-fly and (3) computes each new state in polynomial time--this last point is crucial as it guarantees that the running time is polynomial in the size of the output automaton. Then, we show how to apply this framework for partial disambiguation: by changing the criterion that builds the new states, we develop algorithms for different levels of ambiguity, namely, finitely ambiguous, and polynomially ambiguous automata. These algorithms also satisfy condition (1) for their respective levels, and also (2) and (3). Finally, we show that the disambiguation framework can easily be extended to other models of automata like weighted automata.
