Related papers: The falsification by fellow traveler property impl…
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 furnish an example of a finite generating set for a group that does not enjoy the falsification by fellow traveler property, while the full language of geodesics is regular.
We prove that any Artin group of large type is shortlex automatic with respect to its standard generating set, and that the set of all geodesic words over the same generating set satisfies the Falsification by Fellow-Traveller Property…
Let $W$ be a $2$-dimensional Coxeter group, that is, a one with $\frac{1}{m_{st}}+\frac{1}{m_{sr}}+\frac{1}{m_{tr}}\leq 1$ for all triples of distinct $s,t,r\in S$. We prove that $W$ is biautomatic. We do it by showing that a natural…
Autostackability for finitely presented groups is a topological property of the Cayley graph combined with formal language theoretic restrictions, that implies solvability of the word problem. The class of autostackable groups is known to…
Autostackability for finitely generated groups is defined via a topological property of the associated Cayley graph which can be encoded in a finite state automaton. Autostackable groups have solvable word problem and an effective inductive…
We show that groups presented by inverse-closed finite convergent length-reducing rewriting systems are characterised by a striking geometric property: their Cayley graphs are geodetic and side-lengths of non-degenerate triangles are…
Given a finitely generated relatively hyperbolic group $G$, we construct a finite generating set $X$ of $G$ such that $(G,X)$ has the `falsification by fellow traveler property' provided that the parabolic subgroups $\{H_\omega\}_{\omega\in…
This paper is devoted to the study of the falsification by fellow-traveller property (FFTP) in Dyer groups. We exhibit a finite generating set for which the associated Cayley graph is a locally finite mediangle graph, and leverage its…
Stackability for finitely presented groups consists of a dynamical system that iteratively moves paths into a maximal tree in the Cayley graph. Combining with formal language theoretic restrictions yields auto- or algorithmic stackability,…
We prove that groups enjoying the falsification by fellow traveler property are of type $F_3$, and have at most an exponential second order isoperimetric function.
We prove that a group is presented by finite convergent length-reducing rewriting systems where each rule has left-hand side of length 3 if and only if the group is plain. Our proof goes via a new result concerning properties of embedded…
Models of a generalized nondeterminism are defined by limitations on nonde- terministic behavior of a computing device. A regular realizability problem is a problem of verifying existence of a special sort word in a regular language. These…
In this paper we study rewriting systems for groups and monoids, focusing on situations where finite convergent systems may be difficult to find or do not exist. We consider systems which have no length increasing rules and are confluent…
Higher-order pushdown systems and ground tree rewriting systems can be seen as extensions of suffix word rewriting systems. Both classes generate infinite graphs with interesting logical properties. Indeed, the model-checking problem for…
We introduce a topological property for finitely generated groups called stackable that implies the existence of an inductive procedure for constructing van Kampen diagrams with respect to a particular finite presentation. We also define…
In this article we continue the study of automorphism groups of constant length substitution shifts and also their topological factors. We show that up to conjugacy, all roots of the identity map are letter exchanging maps, and all other…
We introduce an extension of the fellow traveler property which allows fellow travelers to be at distance bounded from above by a function $f(n)$ growing slower than any linear function. We study normal forms satisfying this extended fellow…
The compactness phenomenon is one of the featured aspects of structuralism in mathematics. In simple and broad words, a compactness property holds in a structure if a related property is satisfied by sufficiently many substructures of that…
A group is combable if it can be represented by a language of words satisfying a fellow traveller property; an automatic group has a synchronous combing which is a regular language. This paper gives a systematic analysis of the properties…