Decomposition theorems and model-checking for the modal μ-calculus

M. Bojanczyk, Christoph Dittmann, S. Kreutzer
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引用次数: 8

Abstract

We prove a general decomposition theorem for the modal μ-calculus Lμ in the spirit of Feferman and Vaught's theorem for disjoint unions. In particular, we show that if a structure (i.e., transition system) is composed of two substructures M1 and M2 plus edges from M1 to M2, then the formulas true at a node in M only depend on the formulas true in the respective substructures in a sense made precise below. As a consequence we show that the model-checking problem for Lμ is fixed-parameter tractable (fpt) on classes of structures of bounded Kelly-width or bounded DAG-width. As far as we are aware, these are the first fpt results for Lμ which do not follow from embedding into monadic second-order logic.
模态μ微积分的分解定理和模型检验
我们在费弗曼定理和沃特定理的精神上,证明了模态μ-微积分Lμ的一般分解定理。特别是,我们表明,如果一个结构(即过渡系统)是由两个子结构M1和M2加上从M1到M2的边组成的,那么在M中的一个节点上成立的公式仅依赖于在相应子结构上成立的公式,其意义如下所述。结果表明,Lμ的模型检验问题在有界kelly宽度或有界dag宽度的结构类上是固定参数可处理的(fpt)。据我们所知,这些是Lμ的第一个fpt结果,而不是从嵌入到一元二阶逻辑中得到的。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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