正则语言的等价性检验
Testing the Equivalence of Regular Languages
摘要：
最小确定性有限自动机通常用于判定正则语言的相等性。Antimirov和Mosses提出了一个重写系统来决定正则表达式的等价性，Almeida等人提出了一个改进的变体。Hopcroft和Karp提出了一个几乎线性的算法来测试两个确定性有限自动机的等价性，避免了最小化。在本文中，我们改进了最佳情况下的运行时间，提出了一个扩展的非确定性有限自动机的算法，并建立了该算法之间的关系，提出了在Almeida等人，我们还提出了一些实验比较结果。这些算法都与Rutten提出的自动机的共代数方法密切相关。
英文摘要：
The minimal deterministic finite automaton is generally used to determine regular languages equality. Antimirov and Mosses proposed a rewrite system for deciding regular expressions equivalence of which Almeida et al. presented an improved variant. Hopcroft and Karp proposed an almost linear algorithm for testing the equivalence of two deterministic finite automata that avoids minimisation. In this paper we improve the best-case running time, present an extension of this algorithm to non-deterministic finite automata, and establish a relationship between this algorithm and the one proposed in Almeida et al. We also present some experimental comparative results. All these algorithms are closely related with the recent coalgebraic approach to automata proposed by Rutten.
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