符号自动机的最小化

Loris D'antoni, Margus Veanes
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引用次数: 93

摘要

符号自动机通过使用符号字母代替有限字母来扩展经典自动机。大多数经典的自动机算法依赖于字母表是有限的,将它们推广到符号设置并不是一项简单的任务。本文研究了符号自动机的最小化问题。我们形式化地定义并证明了符号环境下极小性的基本性质,并将经典的最小化算法(Huffman-Moore算法和Hopcroft算法)提升到符号自动机。虽然Hopcroft的算法是已知最快的DFA最小化算法,但我们展示了在符号字母存在的情况下,它如何导致指数级爆炸。为了解决这个问题,我们引入了一种新的算法,它充分受益于字母表的符号表示,并且不会受到指数膨胀的影响。我们在大型基准测试和现有最先进的实现上对所有算法进行了全面的性能评估。实验表明,新的符号算法比以前的实现更快。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Minimization of symbolic automata
Symbolic Automata extend classical automata by using symbolic alphabets instead of finite ones. Most of the classical automata algorithms rely on the alphabet being finite, and generalizing them to the symbolic setting is not a trivial task. In this paper we study the problem of minimizing symbolic automata. We formally define and prove the basic properties of minimality in the symbolic setting, and lift classical minimization algorithms (Huffman-Moore's and Hopcroft's algorithms) to symbolic automata. While Hopcroft's algorithm is the fastest known algorithm for DFA minimization, we show how, in the presence of symbolic alphabets, it can incur an exponential blowup. To address this issue, we introduce a new algorithm that fully benefits from the symbolic representation of the alphabet and does not suffer from the exponential blowup. We provide comprehensive performance evaluation of all the algorithms over large benchmarks and against existing state-of-the-art implementations. The experiments show how the new symbolic algorithm is faster than previous implementations.
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