Related papers: Computability of Pressure for Subshifts on Countab…
The Rains relative entropy of a bipartite quantum state is the tightest known upper bound on its distillable entanglement -- which has a crisp physical interpretation of entanglement as a resource -- and it is efficiently computable by…
We show that every infinite, locally finite, and connected graph admitsa translation-like action by $\mathbb{Z}$, and that this action can be takento be transitive exactly when the graph has either one or two ends.The actions constructed…
This paper presents a new abstract method for proving lower bounds in computational complexity. Based on the notion of topological and measurable entropy for dynamical systems, it is shown to generalise three previous lower bounds results…
We provide requirements on effectively enumerable topological spaces which guarantee that the Rice-Shapiro theorem holds for the computable elements of these spaces. We show that the relaxation of these requirements leads to the classes of…
In this paper, we study the properties of the scaled packing topological pressures for topological dynamical system $(X,G)$, where $G$ is a countable discrete infinite amenable group. We show that the scaled packing topological pressures…
In this paper, we consider a Borel measurable map of a compact metric space which admits an inducing scheme. Under the finite weighted complexity condition, we establish a thermodynamic formalism for a parameter family of potentials…
Let $\Lambda$ be a compact locally maximal invariant set of a $C^2$-diffeomorphism $f:M\to M$ on a smooth Riemannian manifold $M$. In this paper we study the topological pressure $P_{\rm top}(\phi)$ (with respect to the dynamical system…
Any coded subshift X defined by a set C of code words contains a subshift, which we call L, consisting of limits of single code words. We show that when C satisfies a unique decomposition property, the topological entropy h(X) of X is…
Sofic shifts are symbolic dynamical systems defined by the set of bi-infinite sequences on an edge-labeled directed graph, called a presentation. We study the computational complexity of an array of natural decision problems about…
A computably presented algebraic field $F$ has a \emph{splitting algorithm} if it is decidable which polynomials in $F[X]$ are irreducible there. We prove that such a field is computably categorical iff it is decidable which pairs of…
A semi-computable set S in a computable metric space need not be computable. However, in some cases, if S has certain topological properties, we can conclude that S is computable. It is known that if a semi-computable set S is a compact…
We study the thermodynamic formalism for particular types of sub-additive sequences on a class of subshifts over countable alphabets. The subshifts we consider include factors of irreducible countable Markov shifts under certain conditions.…
The anthropic principle is an inevitable constraint on the space of possible theories. As such it is central to determining the limits of physics. In particular, we contend that what is ultimately possible in physics is determined by…
In this paper, continuous binary operations of a topological space are studied and a criterion of their invertibility is proved. The classification problem of groups of invertible continuous binary operations of locally compact and locally…
One of the fundamental results in computability is the existence of well-defined functions that cannot be computed. In this paper we study the effects of data representation on computability; we show that, while for each possible way of…
Various limit-free formulas are given for the computation of the algebraic and the topological entropy, respectively in the settings of endomorphisms of locally finite discrete groups and of continuous endomorphisms of totally disconnected…
We study theoretical and computational properties of the pressure function for subshifts of finite type on the integer lattice $\Z^d$, multidimensional SOFT, which are called Potts models in mathematical physics. We show that the pressure…
We prove that the entropy map for countable Markov shifts of finite entropy is upper semi-continuous at ergodic measures. Note that the phase space is non-compact. Applications to systems that can be coded by these shifts, such as positive…
For any fixed alphabet A, the maximum topological entropy of a Z^d subshift with alphabet A is obviously log |A|. We study the class of nearest neighbor Z^d shifts of finite type which have topological entropy very close to this maximum,…
We consider interpretable topological spaces and topological groups in a $p$-adically closed field $K$. We identify a special class of "admissible topologies" with topological tameness properties like generic continuity, similar to the…