Related papers: Efficient Compression in Semigroups
The Hidden Subgroup Problem is used in many quantum algorithms such as Simon's algorithm and Shor's factoring and discrete log algorithms. A polynomial time solution is known in case of abelian groups, and normal subgroups of arbitrary…
In this note, we announce the first results on quasi-isometric rigidity of non-nilpotent polycyclic groups. In particular, we prove that any group quasi-isometric to the three dimenionsional solvable Lie group Sol is virtually a lattice in…
Submodular function minimization (SFM) is a fundamental and efficiently solvable problem class in combinatorial optimization with a multitude of applications in various fields. Surprisingly, there is only very little known about constraint…
The group isomorphism problem asks whether two given groups are isomorphic or not. Whereas the case where both groups are abelian is well understood and can be solved efficiently, very little is known about the complexity of isomorphism…
In this paper, we show that the constant-dimensional Weisfeiler-Leman algorithm for groups (Brachter & Schweitzer, LICS 2020) can be fruitfully used to improve parallel complexity upper bounds on isomorphism testing for several families of…
We present a general diagrammatic approach to the construction of efficient algorithms for computing the Fourier transform of a function on a finite group. By extending work which connects Bratteli diagrams to the construction of Fast…
Let $G$ be an infinite simple group of finite Morley rank and $\alpha$ a supertight automorphism of $G$ so that the fixed point subgroup $P_n:=C_G(\alpha^n)$ is pseudofinite for all $n\in \mathbb{N}\setminus\{0\}$. It is know (using CFSG)…
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…
We study the problem of finding a subgroup of a given order in a finite group, where the group is represented by its Cayley table. We analyze the complexity of the problem in the special case of abelian groups and present an optimal…
Semidefinite programming is a powerful tool in the design and analysis of approximation algorithms for combinatorial optimization problems. In particular, the random hyperplane rounding method of Goemans and Williamson has been extensively…
We study the fine-grained complexity of evaluating Boolean Conjunctive Queries and their generalization to sum-of-product problems over an arbitrary semiring. For these problems, we present a general semiring-oblivious reduction from the…
This work presents a precise connection between Clifford circuits, Shor's factoring algorithm and several other famous quantum algorithms with exponential quantum speed-ups for solving Abelian hidden subgroup problems. We show that all…
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…
We investigate the properties of a system of semi-diluted polymers in the presence of charged groups and counter-ions, by means of self-consistent field theory. We study a system of polyelectrolyte chains grafted to a similarly, as well as…
Sofic and hyperlinear groups are the countable discrete groups that can be approximated in a suitable sense by finite symmetric groups and groups of unitary matrices. These notions turned out to be very deep and fruitful, and stimulated in…
Semidefinite programming (SDP) is a powerful tool for tackling a wide range of computationally hard problems such as clustering. Despite the high accuracy, semidefinite programs are often too slow in practice with poor scalability on large…
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…
Symmetry handling inequalities (SHIs) are an appealing and popular tool for handling symmetries in integer programming. Despite their practical application, little is known about their interaction with optimization problems. This article…
The discrete logarithm problem in Jacobians of curves of high genus $g$ over finite fields $\FF_q$ is known to be computable with subexponential complexity $L_{q^g}(1/2, O(1))$. We present an algorithm for a family of plane curves whose…
Functions on a bounded domain in scientific computing are often approximated using piecewise polynomial approximations on meshes that adapt to the shape of the geometry. We study the problem of function approximation using splines on a…