Related papers: Dynamic Complexity of Group Problems
Dynamic Complexity was introduced by Immerman and Patnaik \cite{PatnaikImmerman97} (see also \cite{DongST95}). It has seen a resurgence of interest in the recent past, see…
Patnaik and Immerman introduced the dynamic complexity class DynFO of database queries that can be maintained by first-order dynamic programs with the help of auxiliary relations under insertions and deletions of edges (Patnaik and Immerman…
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…
Dynamic complexity is concerned with updating the output of a problem when the input is slightly changed. We study the dynamic complexity of model checking a fixed monadic second-order formula over evolving subgraphs of a fixed maximal…
Dynamic complexity is concerned with updating the output of a problem when the input is slightly changed. We study the dynamic complexity of Dyck reachability problems in directed and undirected graphs, where updates may add or delete…
Dynamic Complexity (as introduced by Patnaik and Immerman) tries to express how hard it is to update the solution to a problem when the input is changed slightly. It considers the changes required to some stored data structure (possibly a…
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…
The Dynamical Graph Grammar (DGG) formalism can describe complex system dynamics with graphs that are mapped into a master equation. An exact stochastic simulation algorithm may be used, but it is slow for large systems. To overcome this…
Existentially closed groups are, informally, groups that contain solutions to every consistent finite system of equations and inequations. They were introduced in 1951 in an algebraic context and subsequent research elucidated deep…
The article investigates classes of queries maintainable by conjunctive queries (CQs) and their extensions and restrictions in the dynamic complexity framework of Patnaik and Immerman. Starting from the basic language of quantifier-free…
We study deterministic and quantum dynamics from a constructive "finite" point of view, since the introduction of a continuum, or other actual infinities in physics poses serious conceptual and technical difficulties, without any need for…
This article surveys the burgeoning area at the intersection of dynamical systems theory and algorithms for NP-hard problems. Traditionally, computational complexity and the analysis of non-deterministic polynomial-time (NP)-hard problems…
Problems based on the structure of graphs -- for example finding cliques, independent sets, or colourings -- are of fundamental importance in classical complexity. Defining well-formulated decision problems for quantum graphs, which are an…
Let $G$ be a finite group given as input by its multiplication table. For a subset $S$ of $G$ and an element $g\in G$ the Cayley Group Membership Problem (denoted CGM) is to check if $g$ belongs to the subgroup generated by $S$. While this…
Fractal groups (also called self-similar groups) is the class of groups discovered by the first author in the 80-s of the last century with the purpose to solve some famous problems in mathematics, including the question raising to von…
The dynamic matrix inverse problem is to maintain the inverse of a matrix undergoing element and column updates. It is the main subroutine behind the best algorithms for many dynamic problems whose complexity is not yet well-understood,…
Previous contrastive deep clustering methods mostly focus on instance-level information while overlooking the member relationship within groups/clusters, which may significantly undermine their representation learning and clustering…
Discrete dynamical systems can exhibit complex behaviour from the iterative application of straightforward local rules. A famous example are cellular automata whose global dynamics are notoriously challenging to analyze. To address this, we…
We introduce a discrete 4-dimensional module over the integers that appears to have maximal symmetry. By adjoining the usual Minkowski distance, we obtain a discrete 4-dimensional Minkowski space. Forming universe histories in this space…
We answer two questions on the complexities of decision problems of groups, each related to a classical result. First, C. Miller characterized the complexity of the isomorphism problem for finitely presented groups in 1971. We do the same…