Related papers: Context-Free Groups and Bass-Serre Theory
Proof assistants are software-based tools that are used in the mechanization of proof construction and validation in mathematics and computer science, and also in certified program development. Different tools are being increasingly used in…
A monoid is said to be special if it admits a presentation in which all defining relations are of the form $w = 1$. Groups are familiar examples of special monoids. This article studies the geometric and structural properties of the Cayley…
For a finite connected graph $\mathcal{E}$ with set of edges $E$, a finite $E$-generated group $G$ is constructed such that the set of relations $p=1$ satisfied by $G$ (with $p$ a word over $E\cup E^{-1}$) is closed under deletion of…
Universality has been an important concept in computable structure theory. A class $\mathcal{C}$ of structures is universal if, informally, for any structure, of any kind, there is a structure in $\mathcal{C}$ with the same…
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…
For a subgroup of a free product of finite groups, we obtain necessary conditions (on its Kurosh decomposition) to be verbally closed.
We present a necessary condition for an infinite language to be multiple context-free, which we call a Substitution Lemma. We apply it to show a sample selection of languages are not multiple context-free, including the word problem of the…
This work is a survey of the main results reported for the degree of extension of two models defining non-regular languages, namely the context-free grammar and the extended automaton over groups. More precisely, we recall the main results…
We introduce an algebraic structure for studying state-independent contextuality arguments, a key form of quantum non-classicality exemplified by the well-known Peres-Mermin magic square, and used as a source of quantum advantage. We…
We study the full language of quasigeodesics in Cayley graphs, with fixed error constants. We show that, given a non-virtually-cyclic nilpotent group or Baumslag--Solitar group, and any finite generating set, such languages fail to be…
Although adequate models of human language for syntactic analysis and semantic interpretation are of at least context-free complexity, for applications such as speech processing in which speed is important finite-state models are often…
We prove (using grammars) that the free inverse monoid of every finite rank has co-context-free word problem. Equivalently, the co-word problem of the free inverse monoid of every finite rank is context-free.
We give a complete classification of finitely generated virtually free groups up to $\forall\exists$-elementary equivalence. As a corollary, we give an algorithm that takes as input two finite presentations of virtually free groups, and…
We prove that a group has word problem that is a growing context-sensitive language precisely if its word problem can be solved using a non-deterministic Cannon's algorithm (the deterministic algorithms being defined by Goodman and…
In this paper we study the generic, i.e., typical, behavior of finitely generated subgroups of hyperbolic groups and also the generic behavior of the word problem for amenable groups. We show that a random set of elements of a nonelementary…
We show the existence of finitely presented torsion-free groups with decidable word problem that cannot be embedded in any finitely generated group with decidable conjugacy problem. This answers a well-known question of Collins from the…
We give in this paper a logical characterization for unambiguous Context Free Languages, in the vein of descriptive complexity. A fragment of the logic characterizing context free languages given by Lautemann, Schwentick and Th\'erien [18]…
We study fibers of word maps in finite, profinite, and residually finite groups. Our main result is that, for any word w in the free group on d generators, there exists $\epsilon > 0$ such that if G is a residually finite group with…
In this paper we consider some results obtained for graphs using minimal vertex separators and generalized chordality and translate them to the context of Geometric Group Theory. Using these new tools, we are able to give two new…
A free Steiner quasigroup is a free object in the variety of Steiner quasigroups. Free Steiner quasigroups are characterised by the existence of a levelled construction that starts with a free base - that is, a set of elements none of which…