Related papers: On semi-open codes and bi-continuing almost everyw…
Given an irreducible sofic shift X, we show that an an irreducible SFT Y of lower entropy is a factor of X if and only if it is a factor of X by an open bi-continuing code. If these equivalent conditions hold and Y is mixing, then any code…
We investigate what happens when we try to work with continuing block codes (i.e. left or right continuing factor maps) between shift spaces that may not be shifts of finite type. For example, we demonstrate that continuing block codes on…
A subclass of coded systems containing synchronized systems is the family of half-synchronized systems. In this note, we will consider them and show that the property half-synchronized lifts under hyperbolic maps. This enables us to define…
We define class-closing factor codes from shifts of finite type and show that they are continuing if their images are of finite type. We establish several relations between class-closing factor codes, continuing factor codes and…
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…
It is shown that if an infinite synchronized system has a flip, then it has infinitely many non-conjugate flips, and that the result cannot be extended to the class of coded systems.
The purpose of this paper is to find conditions for a continuous onto map $\phi\colon X\rightarrow Y$ and its induced map $\phi_*\colon\mathcal{M}^1(X)\rightarrow\mathcal{M}^1(Y)$ to be semi-open, where $X$, $Y$ are compact Hausdorff spaces…
Given two graphs G and H, there is a bi-resolving (or bi-covering) graph homomorphism from G to H if and only if their adjacency matrices satisfy certain matrix relations. We investigate the bi-covering extensions of bi-resolving…
We study limit sets of stable cellular automata standing from a symbolic dynamics point of view where they are a special case of sofic shifts admitting a steady epimorphism. We prove that there exists a right-closing almost-everywhere…
We prove that the semigroup operation of a topological semigroup $S$ extends to a continuous semigroup operation on its the Stone-\v{C}ech compactification $\beta S$ provided $S$ is a pseudocompact openly factorizable space, which means…
We show that a synchronized coded system $X$ is intrinsically ergodic of full support if and only if $ h(Y)$, the topological entropy of $Y$, is less than $h(X) $ whenever $Y$ is a proper subsystem of $ X $. We also show that like systems…
We show that the synchronized states of two systems of identical chaotic maps subject to either, a common drive that acts with a probability p in time or to the same drive acting on a fraction p of the maps, are similar. The synchronization…
Given a factor code between sofic shifts X and Y, there is a family of decompositions of the original code into factor codes such that the entropies of the intermediate subshifts arising from the decompositions are dense in the interval…
In this paper we study the asymptotic behaviour of two relatively new complexity functions defined on infinite words and their relationship to periodicity. Given a factor $u$ of an infinite word $x$, we say $u$ is closed if it is a letter…
Given a factor code $\pi$ from a shift of finite type $X$ onto a sofic shift $Y$, the class degree of $\pi$ is defined to be the minimal number of transition classes over points of $Y$. In this paper we investigate structure of transition…
We show that a coded system is mixing if and only if it is totally transitive and if in addition it has a relatively prime generator, then it has strong property P. We continue by showing that a mixing half-synchronized system has such a…
Some type-based approaches to termination use sized types: an ordinal bound for the size of a data structure is stored in its type. A recursive function over a sized type is accepted if it is visible in the type system that recursive calls…
Generalizing a result of MacDonald we give necessary and sufficient conditions for an arbitrary subshift to embed into an irreducible sofic shift factoring through a given cover by an irreducible subshift of finite type (SFT). We obtain…
Formal verification using the model checking paradigm has to deal with two aspects: The system models are structured, often as products of components, and the specification logic has to be expressive enough to allow the formalization of…
In this paper we give conditions under which a topological semigroup can be embedded algebraically and topologically into a compact topological group. We prove that every feebly compact regular first countable cancellative commutative…