Related papers: Decision problems for word-hyperbolic semigroups
In this paper we investigate Gromov's question: whether every one-ended word hyperbolic group contains a surface subgroup. The case of double groups is considered by studying the associated one relator groups. We show that the majority…
We show that superreflexivity can be characterized in terms of bilipschitz embeddability of word hyperbolic groups. We compare characterizations of superreflexivity in terms of diamond graphs and binary trees. We show that there exist…
The Whitehead minimization problem consists in finding a minimum size element in the automorphic orbit of a word, a cyclic word or a finitely generated subgroup in a finite rank free group. We give the first fully polynomial algorithm to…
The study of verbal subgroups within a group is well-known for being an effective tool to obtain structural information about a group. Therefore, conditions that allow the classification of words in a free group are of paramount importance.…
This paper deals with the decidability of semigroup freeness. More precisely, the freeness problem over a semigroup S is defined as: given a finite subset X of S, decide whether each element of S has at most one factorization over X. To…
The asymptotic bound for a length-based attack on the Conjugacy Search Problem in relatively hyperbolic groups is cubic for hyperbolic elements and a "small" polynomial for parabolic elements, depending on the Conjugacy Search Problem for…
We propose a way of associating to each finitely generated monoid or semigroup a formal language, called its loop problem. In the case of a group, the loop problem is essentially the same as the word problem in the sense of combinatorial…
We give an algorithm for solving equations and inequations with rational constraints in virtually free groups. Our algorithm is based on Rips classification of measured band complexes. Using canonical representatives, we deduce an algorithm…
We exhibit examples of finitely presented subgroups $P$ of direct products of hyperbolic groups for which there is no algorithm that detects whether a finitely presented group has a quotient isomorphic to $P$. For any torsion-free, linear,…
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…
Let $\mathrm{WP}_G$ denote the word problem in a finitely generated group $G$. We consider the complexity of $\mathrm{WP}_G$ with respect to standard deterministic Turing machines. Let $\mathrm{DTIME}_k(t(n))$ be the complexity class of…
We give a simple algorithm to solve the subgroup membership problem for virtually free groups. For a fixed virtually free group with a fixed generating set $X$, the subgroup membership problem is uniformly solvable in time $O(n\log^*(n))$…
Recently the third named author defined a 2-parametric family of groups $G_n^k$ \cite{gnk}. Those groups may be regarded as a certain generalisation of braid groups. Study of the connection between the groups $G_n^k$ and dynamical systems…
The word problem for Thompson's group $F$ has a solution, but it remains unknown whether $F$ is automatic or has a finite or regular convergent (terminating and confluent) rewriting system. We show that the group $F$ admits a natural…
We implement a decision procedure for answering questions about a class of infinite words that might be called (for lack of a better name) "Fibonacci-automatic". This class includes, for example, the famous Fibonacci word f = 01001010...,…
The word problem for categories with free products and coproducts (sums), SP-categories, is directly related to the problem of determining the equivalence of certain processes. Indeed, the maps in these categories may be directly…
This thesis investigates the central role of homomorphism problems (structure-preserving maps) in two complementary domains: database querying over finite, graph-shaped data, and constraint solving over (potentially infinite) structures.…
For any group, there is a natural (pseudo-)norm on the vector space B1 of real (group) 1-boundaries, called the stable commutator length norm. This norm is closely related to, and can be thought of as a relative version of, the Gromov…
We study the Identity Problem, the problem of determining if a finitely generated semigroup of matrices contains the identity matrix; see Problem 3 (Chapter 10.3) in ``Unsolved Problems in Mathematical Systems and Control Theory'' by…
We study conjugacy classes of solutions to systems of equations and inequations over torsion-free hyperbolic groups, and describe an algorithm to recognize whether or not there are finitely many conjugacy classes of solutions to such a…