Related papers: The extended future cover of a sofic shift
The paper contains a new proof of the theorem by Krieger which establishes the canonicity of the future cover of a sofic shift. In addition the paper describes a method to produce new canonical covers from a given one, resulting in…
A canonical cover generalizing the left Fischer cover to arbitrary sofic shifts is introduced and used to prove that the left Krieger cover and the past set cover of a sofic shift can be divided into natural layers. These results are used…
A notion known as smooth envelope, or superposition closure, appears naturally in several approaches to generalized smooth manifolds which were proposed in the last decades. Such an operation is indispensable in order to perform…
We define a pair of simple combinatorial operations on subshifts, called existential and universal extensions, and study their basic properties. We prove that the existential extension of a sofic shift by another sofic shift is always…
The covering radius of a shift space is a quantity of interest for information-theoretic applications of data transmission over noisy channels. We prove that the covering radius of a primitive sofic shift is a rational number, and describe…
As a variant of the equal entropy cover problem, we ask whether all multidimensional sofic shifts with countably many configurations have SFT covers with countably many configurations. We answer this question in the negative by presenting…
This paper gives a systematic construction of certain covers of finite semigroups. These covers will be used in future work on the complexity of finite semigroups.
We develop the theory of Schur covers of finite skew braces. We prove the existence of at least one Schur cover. We also compute several examples. We prove that different Schur covers are isoclinic. Finally, we prove that Schur covers have…
We present an improved version of the cyclic covering trick, which works inside the category of toroidal embeddings
This is a survey on the ongoing development of a descriptive theory of represented spaces, which is intended as an extension of both classical and effective descriptive set theory to deal with both sets and functions between represented…
We consider the future causal boundary as a tool to find obstructions to conformal extensions, the latter being a slight generalization to conformal compactifications.
This is not in any way meant to be a complete survey on positive curvature. Rather it is a short essay on the fascinating changes in the landscape surrounding positive curvature. In particular, details and many results and references are…
We summarise the new conformal framework of an Anisotropic Future Endless Universe and an Anisotropic Future Singularity. Both new definitions are motivated by, but not restricted to quiescent cosmology and the Weyl curvature hypothesis,…
Given a code from a shift space to an irreducible sofic shift, any two of the following three conditions -- open, constant-to-one, (right or left) closing -- imply the third. If the range is not sofic, then the same result holds when…
The fundamental groupoid of a space becomes enriched over the category of topological spaces when the hom-sets are endowed with topologies intimately related to universal constructions of topological groups. This paper is devoted to a…
The paraxial approximation of a classical spinning photon is shown to yield an "exotic particle" in the plane transverse to the propagation. The previously proposed and observed position shift between media with different refractive indices…
The flow equivalence of sofic shifts is examined using results about the structure of the corresponding covers. A canonical cover generalising the left Fischer cover to arbitrary sofic shifts is introduced and used to prove that the left…
This work is a continuation of our previous works concerning linear canonical transformations and phase space representation of quantum theory. It is mainly focused on the description of an approach which allows to establish spinorial…
We discuss the future evolution of the universe in the light of recent observations. The apparent luminosity vs. redshift of supernovae favor an accelerating universe. However an Einstein-de Sitter critical universe should not be ruled out…
We will show that a system is synchronized if and only if it has a cover whose cover map is semi-open. Also, any factor code on an irreducible sofic shift is semi-open and the image of a synchronized system by a semi-open code is…