可分解拟阵上的一元二阶模型检验
Monadic second-order model-checking on decomposable matroids
摘要：
一个概念的分支宽度，这推广了一个已知的图，可以定义为拟阵。本文首先证明了一元二阶公式在有界分支宽度的可表示拟阵上的多项式时间模型检验，并将其约简为树上的一元二阶公式。这个证明比以前已知的要简单得多。我们还提供了我们的逻辑方法和语法，允许建立有界分支宽度拟阵之间的联系。最后，我们引入了一类新的不一定表示拟阵，描述的文法和一元二阶公式可以检查线性时间。
英文摘要：
A notion of branch-width, which generalizes the one known for graphs, can be defined for matroids. We first give a proof of the polynomial time model-checking of monadic second-order formulas on representable matroids of bounded branch-width, by reduction to monadic second-order formulas on trees. This proof is much simpler than the one previously known. We also provide a link between our logical approach and a grammar that allows to build matroids of bounded branch-width. Finally, we introduce a new class of non-necessarily representable matroids, described by a grammar and on which monadic second-order formulas can be checked in linear time.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
