可达性在DynFO中

The Dynamic Complexity of Acyclic Hypergraph Homomorphisms

Finding a homomorphism from some hypergraph $\mathcal{Q}$ (or some relational structure) to another hypergraph $\mathcal{D}$ is a fundamental problem in computer science. We show that an answer to this problem can be maintained under single-edge changes of $\mathcal{Q}$, as long as it stays acyclic, in the DynFO framework of Patnaik and Immerman that uses updates expressed in first-order logic. If additionally also changes of $\mathcal{D}$ are allowed, we show that it is unlikely that existence of homomorphisms can be maintained in DynFO.

Reachability and Distances under Multiple Changes

Recently it was shown that the transitive closure of a directed graph can be updated using first-order formulas after insertions and deletions of single edges in the dynamic descriptive complexity framework by Dong, Su, and Topor, and Patnaik and Immerman. In other words, Reachability is in DynFO. In this article we extend the framework to changes of multiple edges at a time, and study the Reachability and Distance queries under these changes. We show that the former problem can be maintained in DynFO$(+, \times)$ under changes affecting O($\frac{\log n}{\log \log n}$) nodes, for graphs with $…

Dynamic Meta-theorems for Distance and Matching

Reachability, distance, and matching are some of the most fundamental graph problems that have been of particular interest in dynamic complexity theory in recent years [DKMSZ18, DMVZ18, DKMTVZ20]. Reachability can be maintained with first-order update formulas, or equivalently in DynFO in general graphs with n nodes [DKMSZ18], even under O(log n/loglog n) changes per step [DMVZ18]. In the context of how large the number of changes can be handled, it has recently been shown [DKMTVZ20] that under a polylogarithmic number of changes, reachability is in DynFOpar in planar, bounded treewidth, and r…

关于在DynFO中可保持的正则语言类的代数刻画

Algebraic Characterizations of Classes of Regular Languages in DynFO

本文研究了在DynFO框架下，通过一阶逻辑片段保持正则语言类的代数特性，并改进了相关结果。

动态平面嵌入属于 DynFO

Dynamic Planar Embedding is in DynFO

本文证明动态平面嵌入属于 DynFO：通过仅维护三连通分量嵌入及分离对二染色，支持边插入、删除并拒绝破坏平面性的插入。

群问题的动态复杂度

Dynamic Complexity of Group Problems

本文研究群论问题的动态复杂度，提出在 DynFO 中维护群成员与阿贝尔群同构的新技术，包括立方独立序列方法。