A. Weiss
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On the Constant-Depth Circuit Complexity of Generating Quasigroups Open
We investigate the constant-depth circuit complexity of the Isomorphism Problem, Minimum Generating Set Problem (MGS), and Sub(quasi)group Membership Problem (Membership) for groups and quasigroups (=Latin squares), given as input in terms…
Membership and Conjugacy in Inverse Semigroups Open
The membership problem for an algebraic structure asks whether a given element is contained in some substructure, which is usually given by generators. In this work we study the membership problem, as well as the conjugacy problem, for fin…
On the complexity of epimorphism testing with virtually abelian targets Open
Friedl and Löh (2021, Confl. Math.) prove that testing whether or not there is an epimorphism from a finitely presented group to a virtually cyclic group, or to the direct product of an abelian and a finite group, is decidable. Here we pro…
Violating Constant Degree Hypothesis Requires Breaking Symmetry Open
The Constant Degree Hypothesis was introduced by Barrington et. al. [David A. Mix Barrington et al., 1990] to study some extensions of q-groups by nilpotent groups and the power of these groups in a computation model called NuDFA (non-unif…
Spatially Resolved Transcriptomics Data Clustering with Tailored Spatial-scale Modulation Open
Spatial transcriptomics, comprising spatial location and high-throughput gene expression information, provides revolutionary insights into disease discovery and cellular evolution. Spatial transcriptomic clustering, which pinpoints distinc…
Constant Depth Circuit Complexity for Generating Quasigroups Open
We investigate the constant-depth circuit complexity of the Isomorphism Problem, Minimum Generating Set Problem (MGS), and Sub(quasi)group Membership Problem (Membership) for groups and quasigroups (=Latin squares), given as input in terms…
Finite groups with geodetic Cayley graphs Open
A connected undirected graph is called \emph{geodetic} if for every pair of vertices there is a unique shortest path connecting them. It has been conjectured that for finite groups, the only geodetic Cayley graphs are odd cycles and comple…
On the Constant-Depth Circuit Complexity of Generating Quasigroups Open
We investigate the constant-depth circuit complexity of the Isomorphism Problem, Minimum Generating Set Problem (MGS), and Sub(quasi)group Membership Problem (Membership) for groups and quasigroups (=Latin squares), given as input in terms…
Parallel algorithms for power circuits and the word problem of the Baumslag group Open
Power circuits have been introduced in 2012 by Myasnikov, Ushakov and Won as a data structure for non-elementarily compressed integers supporting the arithmetic operations addition and $$(x,y) \mapsto x\cdot 2^y$$ . The same …
Complexity of Spherical Equations in Finite Groups Open
In this paper we investigate computational properties of the Diophantine problem for spherical equations in some classes of finite groups. We classify the complexity of different variations of the problem, e.g., when $G$ is fixed and when …
Geodetic Graphs: Experiments and New Constructions Open
In 1962 Ore initiated the study of geodetic graphs. A graph is called geodetic if the shortest path between every pair of vertices is unique. In the subsequent years a wide range of papers appeared investigating their peculiar properties. …
Improved Parallel Algorithms for Baumslag Groups Open
The Baumslag group had been a candidate for a group with an extremely difficult word problem until Myasnikov, Ushakov, and Won succeeded to show that its word problem can be solved in polynomial time. Their result used the newly developed …
Lower Bounds for Sorting 16, 17, and 18 Elements Open
It is a long-standing open question to determine the minimum number of comparisons $S(n)$ that suffice to sort an array of $n$ elements. Indeed, before this work $S(n)$ has been known only for $n\leq 22$ with the exception for $n=16$, $17$…
Dynamic Stall Investigation on a Rotating semi-elastic Double-swept Rotor Blade at the Rotor Test Facility Gottingen Open
Experimental investigations of three-dimensional dynamic stall on a four-bladed Mach-scaled semi-elastic rotor with an innovative double-swept rotor blade planform are presented. The study focuses on the coupling between the aeroelastic be…
An Automaton Group with PSPACE-Complete Word Problem Open
We construct an automaton group with a -complete word problem, proving a conjecture due to Steinberg. Additionally, the constructed group has a provably more difficult, namely -complete, compressed word problem and acts over a binary alpha…
The Power Word Problem in Graph Products Open
The power word problem for a group $G$ asks whether an expression $u_1^{x_1} \cdots u_n^{x_n}$, where the $u_i$ are words over a finite set of generators of $G$ and the $x_i$ binary encoded integers, is equal to the identity of $G$. It is …
View article: The isomorphism problem for plain groups is in $Σ_3^{\mathsf{P}}$
The isomorphism problem for plain groups is in $Σ_3^{\mathsf{P}}$ Open
Testing isomorphism of infinite groups is a classical topic, but from the complexity theory viewpoint, few results are known. S{é}nizergues and the fifth author (ICALP2018) proved that the isomorphism problem for virtually free groups is d…
View article: The isomorphism problem for plain groups is in $\Sigma_3^{\mathsf{P}}$
The isomorphism problem for plain groups is in $\Sigma_3^{\mathsf{P}}$ Open
Testing isomorphism of infinite groups is a classical topic, but from the complexity theory viewpoint, few results are known. S{\'e}nizergues and the fifth author (ICALP2018) proved that the isomorphism problem for virtually free groups is…
Parallel algorithms for power circuits and the word problem of the Baumslag group Open
Power circuits have been introduced in 2012 by Myasnikov, Ushakov and Won as a data structure for non-elementarily compressed integers supporting the arithmetic operations addition and $(x,y) \mapsto x\cdot 2^y$. The same authors applied p…
Parallel Algorithms for Power Circuits and the Word Problem of the Baumslag Group Open
Power circuits have been introduced in 2012 by Myasnikov, Ushakov and Won as a data structure for non-elementarily compressed integers supporting the arithmetic operations addition and (x,y) ↦ x⋅2^y. The same authors applied power circuits…
On the Average Case of MergeInsertion Open
MergeInsertion, also known as the Ford-Johnson algorithm, is a sorting algorithm which, up to today, for many input sizes achieves the best known upper bound on the number of comparisons. Indeed, it gets extremely close to the information-…
Hardness of equations over finite solvable groups under the exponential time hypothesis Open
Goldmann and Russell (2002) initiated the study of the complexity of the equation satisfiability problem in finite groups by showing that it is in P for nilpotent groups while it is NP-complete for non-solvable groups. Since then, several …
Groups with ALOGTIME-Hard Word Problems and PSPACE-Complete Circuit Value Problems Open
We give lower bounds on the complexity of the word problem of certain non-solvable groups: for a large class of non-solvable infinite groups, including in particular free groups, Grigorchuk’s group and Thompson’s groups, we prove that thei…
Hardness of equations over finite solvable groups under the exponential time hypothesis Open
Goldmann and Russell (2002) initiated the study of the complexity of the equation satisfiability problem in finite groups by showing that it is in P for nilpotent groups while it is NP-complete for non-solvable groups. Since then, several …
Groups with ALOGTIME-hard word problems and PSPACE-complete compressed word problems Open
We give lower bounds on the complexity of the word problem of certain non-solvable groups: for a large class of non-solvable infinite groups, including in particular free groups, Grigorchuk's group and Thompson's groups, we prove that thei…