Related papers: Visibly Pushdown Languages in Groups
We show that the decidability of the first-order theory of the language that combines Boolean algebras of sets of uninterpreted elements with Presburger arithmetic operations. We thereby disprove a recent conjecture that this theory is…
We investigate the average-case complexity of decision problems for finitely generated groups, in particular the word and membership problems. Using our recent results on ``generic-case complexity'' we show that if a finitely generated…
We continue the research on the generative capacity of contextual grammars where contexts are adjoined around whole words (externally) or around subwords (internally) which belong to special regular selection languages. All languages…
I investigate modal group theory for arbitrary homomorphisms. Possibility is interpreted by the existence of a group homomorphism out of the given group, so the semantics is governed by the possibility of collapse: elements may be…
We prove that finitely generated free metabelian groups $\Psi_n$ are profinitely rigid in the absolute sense: they are distinguished by their finite quotients among all finitely generated residually finite groups. The proof is based on a…
In this paper we prove several results regarding decidability of the membership problem for certain submonoids in amalgamated free products and HNN extensions of groups. These general results are then applied to solve the prefix membership…
We propose a formalism for representation of finite languages, referred to as the class of IDL-expressions, which combines concepts that were only considered in isolation in existing formalisms. The suggested applications are in natural…
Let $w$ be a group-word. Suppose that the set of all $w$-values in a profinite group $G$ is contained in a union of countably many subgroups. It is natural to ask in what way the structure of the verbal subgroup $w(G)$ depends on the…
We construct words with small image in a given finite alternating or unimodular group. This shows that word width in these groups is unbounded in general.
Classes of algebraic structures that are defined by equational laws are called varieties or equational classes. A variety is finitely generated if it is defined by the laws that hold in some fixed finite algebra. We show that every…
Generalizations of linear numeration systems in which the set of natural numbers is recognizable by finite automata are obtained by describing an arbitrary infinite regular language following the lexicographic ordering. For these systems of…
A class of valued constraint satisfaction problems (VCSPs) is characterised by a valued constraint language, a fixed set of cost functions on a finite domain. An instance of the problem is specified by a sum of cost functions from the…
We consider grammar-restricted exact learning of formulas and terms in finite variable logics. We propose a novel and versatile automata-theoretic technique for solving such problems. We first show results for learning formulas that…
A finitely generated group admits a decomposition, called its Grushko decomposition, into a free product of freely indecomposable groups. There is an algorithm to construct the Grushko decomposition of a finite graph of finite rank free…
Self-similar groups provide a rich source of groups with interesting properties; e.g., infinite torsion groups (Burnside groups) and groups with an intermediate word growth. Various self-similar groups can be described by a recursive…
We study the problem of fitting ontologies and constraints to positive and negative examples that take the form of a finite relational structure. As ontology and constraint languages, we consider the description logics $\mathcal{E\mkern-2mu…
The most developed aspect of the theory of finite semigroups is their classification in pseudovarieties. The main motivation for investigating such entities comes from their connection with the classification of regular languages via…
Let $\Sigma = X\cup X^{-1} = \{ x_1 ,x_2 ,..., x_m ,x_1^{-1} ,x_2^{-1} ,..., x_m^{-1} \}$ and let $G$ be a group with set of generators $\Sigma$. Let $\mathfrak{L} (G) =\left\{ \left. \omega \in \Sigma^* \; \right\vert \;\omega \equiv e \;…
In this paper, we determine the descriptive complexity of subsets of the Polish space of marked groups defined by various group theoretic properties. In particular, using Grigorchuk groups, we establish that the sets of solvable groups,…
We prove several results concerning finitely generated submonoids of the free monoid. These results generalize those known for free submonoids. We prove in particular that if $X=Y\circ Z$ is a composition of finite sets of words with $Y$…