Related papers: Compressed conjugacy and the word problem for oute…
We find polynomial-time solutions to the word problem for free-by-cyclic groups, the word problem for automorphism groups of free groups, and the membership problem for the handlebody subgroup of the mapping class group. All of these…
We prove that the conjugacy problem in right-angled Artin groups (RAAGs), as well as in a large and natural class of subgroups of RAAGs, can be solved in linear-time. This class of subgroups contains, for instance, all graph braid groups…
Many complex questions in biology, physics, and mathematics can be mapped to the graph isomorphism problem and the closely related graph automorphism problem. In particular, these problems appear in the context of network visualization,…
We prove that the conjugacy problem in Out(Fm) is solvable for the class of outer automorphisms whose restrictions to their polynomial subgroups are of finite order. To do this, we first investigate the structure of suspensions of free…
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…
We show that the twisted conjugacy problem is solvable for large-type Artin groups whose outer automorphism group is finite, generated by graph automorphisms and the global inversion. This includes XXXL Artin groups whose defining graph is…
It is well known that the graph isomorphism problem is polynomial-time reducible to the graph automorphism problem (in fact these two problems are polynomial-time equivalent). We show that, analogously, the group isomorphism problem is…
We show that the compressed word problem in a finitely-generated fully residually free group (F -group) is decidable in polynomial time, and use the result to show that the word problem in the automorphism group of such a group is decidable…
We prove that the compressed word problem in a group that is hyperbolic relative to a collection of free abelian subgroups is solvable in polynomial time.
We give a reduction of the conjugacy problem among outer automorphisms of free (and torsion-free hyperbolic) groups to specific algorithmic problems pertaining to mapping tori of polynomially growing automorphisms. We explain how to use…
We describe a constructive, cubic time solution to the conjugacy problem in Artin groups of extra-large type, which was proved solvable in those groups by Appel and Schupp. We use results from two of our previous papers that characterise…
We give a quadratic-time explicit and computable algorithm to solve the word problem for Artin groups that do not contain any relations of length 3. Furthermore, we prove that, given two geodesic words representing the same element, one can…
In this paper we solve the conjugacy problem for several classes of virtual right-angled Artin groups, using algebraic and geometric techniques. We show that virtual RAAGs of the form $A_{\phi} = A_{\Gamma} \rtimes_{\phi}…
We give a simpler proof using automata theory of a recent result of Kapovich, Weidmann and Myasnikov according to which so-called benign graphs of groups preserve decidability of the generalized word problem. These include graphs of groups…
It is shown that the compressed word problem for an HNN-extension with base group H and finite associated subgroups is polynomial time Turing-reducible to the compressed word problem for H. An analogous result for amalgamated free products…
In the past decades for more and more graph classes the Graph Isomorphism Problem was shown to be solvable in polynomial time. An interesting family of graph classes arises from intersection graphs of geometric objects. In this work we show…
In this paper we provide an alternative solution to a result by Juh\'{a}sz that the twisted conjugacy problem for odd dihedral Artin groups is solvable, that is, groups with presentation $G(m) = \langle a,b \; | \; _{m}(a,b) = {}_{m}(b,a)…
The computational complexity of the word problem in HNN-extension of groups is studied. HNN-extension is a fundamental construction in combinatorial group theory. It is shown that the word problem for an ascending HNN-extension of a group H…
We present a solution to the Conjugacy Problem in the group of outer-automorphisms of $F_3$, a free group of rank 3. We distinguish according to several computable invariants, such as irreducibility, subgroups of polynomial growth, and…
We study, from a constructive computational point of view, the techniques used to solve the conjugacy problem in the "generic" lattice-ordered group Aut(R) of order automorphisms of the real line. We use these techniques in order to show…