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Diamond Subgraphs in the Reduction Graph of a One-Rule String Rewriting System
Fundamenta Informaticae ( IF 1.166 ) Pub Date : 2021-01-15 , DOI: 10.3233/fi-2021-2002
Arthur Adinayev 1 , Itamar Stein 2
Affiliation  

In this paper, we study a certain case of a subgraph isomorphism problem. We consider the Hasse diagram of the lattice $M_{k}$ (the unique lattice with $k+2$ elements and one anti-chain of length $k$) and want to find the maximal $k$ for which it is isomorphic to a subgraph of the reduction graph a given one-rule string rewriting system. We obtain a complete characterization for this problem and show that there is a dichotomy. There are one-rule string rewriting systems for which the maximal such $k$ is $2$ and there are cases where there is no maximum. No other intermediate option is possible.

中文翻译:

单规则字符串重写系统的约简图中的菱形子图

在本文中,我们研究了子图同构问题的某个案例。我们考虑格子 $M_{k}$(具有 $k+2$ 个元素和一个长度为 $k$ 的反链的唯一格子)的哈斯图,并想找到它同构的最大 $k$给定的单规则字符串重写系统的归约图的子图。我们获得了这个问题的完整特征,并表明存在二分法。存在单规则字符串重写系统,其中最大的此类 $k$ 为 $2$,并且存在没有最大值的情况。没有其他中间选项是可能的。
更新日期:2021-01-15
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