Related papers: Comparing the Effective Content of Subshifts
We prove that the Steinberg representation of a connected reductive group over an infinite field is irreducible. For finite fields, this is a classical theorem of Steinberg and Curtis.
We apply to logic programming some recently emerging ideas from the field of reduction-based communicating systems, with the aim of giving evidence of the hidden interactions and the coordination mechanisms that rule the operational…
Given a connected reductive group $\tilde{G}$ over a finite field $k$, and a semisimple $k$-automorphism $\varepsilon$ of $\tilde{G}$ of finite order, let $G$ denote the connected part of the group of $\varepsilon$-fixed points. Then there…
We introduce the notion of finitary computable reducibility on equivalence relations on the natural numbers. This is a weakening of the usual notion of computable reducibility, and we show it to be distinct in several ways. In particular,…
We show that the Zink equivalence between p-divisible groups and Dieudonne displays over a complete local ring with perfect residue field of characteristic p is compatible with duality. The proof relies on a new explicit formula for the…
We study the cohomology of symbolic dynamical systems called homshifts: they are the nearest-neighbour $\mathbb{Z}^d$ shifts of finite type whose adjacency rules are the same in every direction. Building on the work of Klaus Schmidt…
Definite descriptions, such as 'the General Chair of KR 2024', are a semantically transparent device for object identification in knowledge representation. In first-order modal logic, definite descriptions have been widely investigated for…
We characterise stable finiteness and pure infiniteness of the essential crossed product of a C*-algebra by an action of an inverse semigroup. Under additional assumptions, we prove a stably finite / purely infinite dichotomy. Our main…
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…
We prove that the Cuntz-Pimsner algebra associated to any surjective aperiodic one-sided subshift with finitely many left special elements has finite nuclear dimension, which is especially the case for every surjective aperiodic subshift…
A coalgebraic definition of finite and infinite trace semantics for probabilistic transition systems has recently been given using a certain Kleisli category. In this paper this semantics is developed using a coalgebraic method which is an…
Natural philosophy integrates scientific observation with abstract frameworks, often using a mathematical Ansatz to hypothesise about physical phenomena. Exploring the possibility of other universes, however, challenges assumptions that…
We study the Monadic Second Order (MSO) Hierarchy over infinite pictures, that is tilings. We give a characterization of existential MSO in terms of tilings and projections of tilings. Conversely, we characterise logic fragments…
We show how finiteness properties of a group and a subgroup transfer to finiteness properties of the Schlichting completion relative to this subgroup. Further, we provide a criterion when the dense embedding of a discrete group into the…
We define a weak notion of universality in symbolic dynamics and, by generalizing a proof of Mike Hochman, we prove that this yields necessary conditions on the forbidden patterns defining a universal subshift: These forbidden patterns are…
For any class of operators which transform unary total functions in the set of natural numbers into functions of the same kind, we define what it means for a real function to be uniformly computable or conditionally computable with respect…
We present a new algorithm deciding if the intersection of a quasiconvex subgroup of a negatively curved group with a conjugate is finite. We also give a short proof of decidability of the membership problem for quasiconvex subgroups of…
We investigate uniform ergodic type theorems for additive and subadditive functions on a subshift over a finite alphabet. We show that every strictly ergodic subshift admits a uniform ergodic theorem for Banach-space-valued additive…
Using approximations, we give several characterizations of separability of bimodules. We also discuss how separability properties can be used to transfer some representation theoretic properties from one ring to another one: contravariant…
Two measures of how near an arbitrary function between groups is to being a homomorphism are considered. These have properties similar to conjugates and commutators. The authors show that there is a rich theory based on these structures,…