为一系列高效的仿真算法奠定基础

Gérard Cécé
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引用次数: 11

摘要

计算初始预订单中包含的最粗模拟预订单用于减少分析给定过渡系统所需的资源。这种技术应用于许多模型,如Kripke结构、标记图、标记转换系统甚至单词和树自动机。设(Q,→)是一个给定的过渡系统,而∑init是对Q的初始预阶。到目前为止,计算∑init中包含的最粗略的模拟,要么是内存高效,要么是时间高效,但不是两者都高效。在本文中,我们提出了一系列有效的仿真算法的基础,并引入了极大转移的概念和预阶相对于粗阶的稳定性的概念。作为一个例子,我们提供了第一个具有最佳公布时间复杂度的算法O(|Psim|.|→|),位空间复杂度为O(|Psim|2.log(|Psim|)+|Q|.log(|Q|)),其中Psim是由∑sim引起的分区,从而解决了一个开放问题。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Foundation for a series of efficient simulation algorithms
Compute the coarsest simulation preorder included in an initial preorder is used to reduce the resources needed to analyze a given transition system. This technique is applied on many models like Kripke structures, labeled graphs, labeled transition systems or even word and tree automata. Let (Q,→) be a given transition system and ℛinit be an initial preorder over Q. Until now, algorithms to compute ℛsim, the coarsest simulation included in ℛinit, are either memory efficient or time efficient but not both. In this paper we propose the foundation for a series of efficient simulation algorithms with the introduction of the notion of maximal transitions and the notion of stability of a preorder with respect to a coarser one. As an illustration we solve an open problem by providing the first algorithm with the best published time complexity, O(|Psim|.|→|), and a bit space complexity in O(|Psim|2.log(|Psim|)+|Q|.log(|Q|)), with Psim the partition induced by ℛsim.
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