Problem
Research questions and friction points this paper is trying to address.
Courcelle's Theorem
tree-width
connection matrices
combinatorial hypothesis
Extensions of Courcelle's Theorem without Logic
🤖 AI Summary
本文通过推广连接矩阵的概念，提出了一种无需逻辑定义的Courcelle定理的广义版本，用于解决图属性检测问题。
📝 Abstract
Courcelle's Theorem states that on graphs $G$ of tree-width at most $k$ with a given tree-decomposition of size $t(G)$, graph properties $\mathcal{P}$ definable in Monadic Second Order Logic can be checked in linear time in the size of $t(G)$. Inspired by L. Lovász' work using connection matrices instead of logic, we give a generalized version of Courcelle's theorem which replaces the definability hypothesis by a purely combinatorial hypothesis using a generalization of connection matrices. This paper clarifies the role of logic in such theorems and displays their purely combinatorial assumption.
Innovation
Methods, ideas, or system contributions that make the work stand out.
generalized version of Courcelle's theorem
purely combinatorial hypothesis
connection matrices
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