相关论文: A Logspace Solution to the Word and Conjugacy prob…
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…
The conjugacy problem belongs to algorithmic group theory. It is the following question: given two words x, y over generators of a fixed group G, decide whether x and y are conjugated, i.e., whether there exists some z such that zxz^{-1} =…
We introduce and study the bounded word problem and the precise word problem for groups given by means of generators and defining relations. For example, for every finitely presented group, the bounded word problem is in NP, i.e., it can be…
We prove that the isomorphism problem is decidable for generalized Baumslag-Solitar (GBS) groups with one quasi-conjugacy class and full support gaps. In order to do so we introduce a family of invariants that fully characterize the…
Generalized Baumslag-Solitar groups (GBS groups) are groups that act on trees with infinite cyclic edge and vertex stabilizers. Such an action is described by a labeled graph (essentially, the quotient graph of groups). This paper addresses…
In various occasions the conjugacy problem in finitely generated amalgamated products and HNN extensions can be decided efficiently for elements which cannot be conjugated into the base groups. This observation asks for a bound on how many…
We present an algorithm to convert a word of length $n$ in the standard generators of the solvable Baumslag-Solitar group $BS(1,p)$ into a geodesic word, which runs in linear time and $O(n\log n)$ space on a random access machine.
In this paper we classify Baumslag-Solitar groups up to commensurability. In order to prove our main result we give a solution to the isomorphism problem for a subclass of Generalised Baumslag-Solitar groups.
For finitely generated nilpotent groups, we employ Mal'cev coordinates to solve several classical algorithmic problems efficiently. Computation of normal forms, the membership problem, the conjugacy problem, and computation of presentations…
We consider three important and well-studied algorithmic problems in group theory: the word, geodesic, and conjugacy problem. We show transfer results from individual groups to graph products. We concentrate on logspace complexity because…
This paper continues the 2012 STACS contribution by Diekert, Ushakov, and the author. We extend the results published in the proceedings in two ways. First, we show that the data structure of power circuits can be generalized to work with…
We discuss the time complexity of the word and conjugacy search problems for free products $G = A \star_C B$ of groups $A$ and $B$ with amalgamation over a subgroup $C$. We stratify the set of elements of $G$ with respect to the complexity…
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…
A generalized Baumslag-Solitar group is a finitely generated group that acts on a tree with infinite-cyclic vertex and edge stabilizers. In this paper, we show that the isomorphism problem is solvable for small rose non-ascending…
We prove that the power word problem for certain metabelian subgroups of $\mathsf{GL}(2,\mathbb{C})$ (including the solvable Baumslag-Solitar groups $\mathsf{BS}(1,q) = \langle a,t \mid t a t^{-1} = a^q \rangle$) belongs to the circuit…
We prove that the compressed word problem and the compressed simultaneous conjugacy problem are solvable in polynomial time in hyperbolic groups. In such problems, group elements are input as words defined by straight line programs defined…
A generalized Baumslag-Solitar (GBS) group is a finitely generated group acting on a tree with infinite cyclic edge and vertex stabilizers. We show how to determine effectively the rank (minimal cardinality of a generating set) of a GBS…
The braid group has recently attracted much attention. This is primarily based upon the discovery of its usage in various cryptosystems [AAG],[KLCHKP]. One major focus of current research has been in solving decision problems in braid…
We consider the rational subset membership problem for Baumslag-Solitar groups. These groups form a prominent class in the area of algorithmic group theory, and they were recently identified as an obstacle for understanding the rational…
Let $\mathcal{C}$ be a class of groups. A group $X$ is said to be residually a $\mathcal{C}$-group (conjugacy $\mathcal{C}$-separable) if, for any elements $x,y \in X$ that are not equal (not conjugate in $X$), there exists a homomorphism…