Related papers: On the Conjugacy Problem in Certain Metabelian Gro…

We give a precise definition of ``generic-case complexity'' and show that for a very large class of finitely generated groups the classical decision problems of group theory - the word, conjugacy and membership problems - all have…

We investigate the computational complexity of various decision problems related to conjugacy in finite inverse semigroups. We describe polynomial-time algorithms for checking if two elements in such a semigroup are ~p conjugate and whether…

We give a classification of irreducible metabelian representations from a knot group into SL(n,C) and GL(n,C). If the homology of the n-fold branched cover of the knot is finite, we show that every irreducible metabelian SL(n,C)…

We give several algorithms addressing computations of intersections of conjugate subgroups.

Multi-homogeneous polynomial systems arise in many applications. We provide bit complexity estimates for solving them which, up to a few extra other factors, are quadratic in the number of solutions and linear in the height of the input…

An element in Artin's braid group B_n is said to be periodic if some power of it lies in the center of B_n. In this paper we prove that all previously known algorithms for solving the conjugacy search problem in B_n are exponential in the…

Evidences have suggested that counting representations are sometimes tractable even when the corresponding classification problem is almost impossible, or "wild" in a precise sense. Such counting problems are directly related to matrix…

We investigate the complexity of isomorphism relations for classes of finitely generated and n-generated computably enumerable (c.e.) algebras, presented via c.e. presentations -- that is, as quotients of term algebras over decidable sets…

We study the problem of matrix Lie algebra conjugacy. Lie algebras arise centrally in areas as diverse as differential equations, particle physics, group theory, and the Mulmuley--Sohoni Geometric Complexity Theory program. A matrix Lie…

Satisfiability of Boolean circuits is among the most known and important problems in theoretical computer science. This problem is NP-complete in general but becomes polynomial time when restricted either to monotone gates or linear gates.…

We consider a combinatorial problem occurring naturally in a group theoretical setting and provide a constructive solution in a special case. More precisely, in 1999 the author established a logarithmic bound for the derived length of the…

Let $\Sigma \subset \mathbb{C}$ be a compact subset of the complex plane, and $\mu$ be a probability distribution on $\Sigma$. We give necessary and sufficient conditions for $\mu$ to be the weak* limit of a sequence of uniform probability…

We study a family of groups consisting of the simplest extensions of lamplighter groups. We use these groups to answer multiple open questions in combinatorial group theory, providing groups that exhibit various combinations of properties:…

Let $G$ be a group endowed with a solution to the conjugacy problem and with an algorithm which computes the centralizer in $G$ of any element of $G$. Let $H$ be a subgroup of $G$. We give some conditions on $H$, under which we provide a…

We classify the computational complexity of the satisfiability, validity and model-checking problems for propositional independence, inclusion, and team logic. Our main result shows that the satisfiability and validity problems for…

We introduce separability properties corresponding to generalized versions of the conjugacy, twisted conjugacy, Brinkmann and Brinkmann's conjugacy problems and how they relate when finite and cyclic extensions of groups are taken. In…

For a fixed $n\ge2$, the Houghton group $H_n$ consists of bijections of $X_n=\{1,\ldots,n\} \times \mathbb{N}$ that are `eventually translations' of each copy of $\mathbb{N}$. The Houghton groups have been shown to have solvable conjugacy…

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…

Part 1 : We remark that the conjugacy problem for pairs of hyperbolic au- tomorphisms of a finitely presented group (typically a free group) is decidable. The solution that we propose uses the isomorphism problem for the suspensions, and…

We introduce the convex combinatorial optimization problem, a far reaching generalization of the standard linear combinatorial optimization problem. We show that it is strongly polynomial time solvable over any edge-guaranteed family, and…