马尔可夫链和无二义自动机

IF 1.1 3区计算机科学 Q1 BUSINESS, FINANCE

Journal of Computer and System Sciences Pub Date : 2023-09-01 DOI:10.1016/j.jcss.2023.03.005

Christel Baier , Stefan Kiefer , Joachim Klein , David Müller , James Worrell

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引用次数: 2

摘要

无歧义自动机是一种不确定性自动机，其中每个单词最多有一个可接受的游程。在本文中，我们给出了一个多项式时间算法，用于针对以模糊自动机表示的ω-正则规范对离散时间马尔可夫链进行模型检查。我们进一步证明了这个模型检验问题的复杂性在于NC：P的子类包括那些在多对数并行时间内可解的问题。这些复杂度边界与根据确定性自动机给出的规范对马尔可夫链进行模型检查的已知边界相匹配，尽管无模糊自动机可以比确定性自动机更简洁。我们报告了我们的过程的实现，包括一个实验，其中该实现用于对马尔可夫链上的LTL公式进行建模检查。

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Markov chains and unambiguous automata

Unambiguous automata are nondeterministic automata in which every word has at most one accepting run. In this paper we give a polynomial-time algorithm for model checking discrete-time Markov chains against ω-regular specifications represented as unambiguous automata. We furthermore show that the complexity of this model checking problem lies in NC: the subclass of P comprising those problems solvable in poly-logarithmic parallel time. These complexity bounds match the known bounds for model checking Markov chains against specifications given as deterministic automata, notwithstanding the fact that unambiguous automata can be exponentially more succinct than deterministic automata. We report on an implementation of our procedure, including an experiment in which the implementation is used to model check LTL formulas on Markov chains.

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来源期刊

Journal of Computer and System Sciences 工程技术-计算机：理论方法

CiteScore

3.70

自引率

0.00%

发文量

审稿时长

68 days

期刊介绍： The Journal of Computer and System Sciences publishes original research papers in computer science and related subjects in system science, with attention to the relevant mathematical theory. Applications-oriented papers may also be accepted and they are expected to contain deep analytic evaluation of the proposed solutions. Research areas include traditional subjects such as: • Theory of algorithms and computability • Formal languages • Automata theory Contemporary subjects such as: • Complexity theory • Algorithmic Complexity • Parallel & distributed computing • Computer networks • Neural networks • Computational learning theory • Database theory & practice • Computer modeling of complex systems • Security and Privacy.