Related papers: The constant of recognizability is computable for …

We give a sharp bound for the automorphism group of a cubic simple graph with a given number of vertices. For each number of vertices we give an explicit graph attaining the bound, and prove its uniqueness in special cases.

We introduce a topology on the space of all isomorphism types represented in a given class of countable models, and use this topology as an aid in classifying the isomorphism types. This mixes ideas from effective descriptive set theory and…

We prove that the maximum speed and the entropy of a one-tape Turing machine are computable, in the sense that we can approximate them to any given precision $\epsilon$. This is contrary to popular belief, as all dynamical properties are…

Let X be an irreducible, primitive complex character of the finite solvable group G, and let X* denote the complex conjugate character. If the degree X(1) is odd, then we show how to associate to X in a unique way, a conjugacy class of…

We relate the computational complexity of finite strings to universal representations of their underlying symmetries. First, Boolean functions are classified using the universal covering topologies of the circuits which enumerate them. A…

The {\em distinguishing number} of a group $G$ acting faithfully on a set $V$ is the least number of colors needed to color the elements of $V$ so that no non-identity element of the group preserves the coloring. The {\em distinguishing…

We define a notion of morphism between combinatorial codes, making the class of all combinatorial codes into a category $\mathbf{Code}$. We show that morphisms can be used to remove redundant information from a code, and that morphisms…

Theories of classification distinguish classes with some good structure theorem from those for which none is possible. Some classes (dense linear orders, for instance) are non-classifiable in general, but are classifiable when we consider…

Classification is a central problem for dynamical systems, in particular for families that arise in a wide range of topics, like substitution subshifts. It is important to be able to distinguish whether two such subshifts are isomorphic,…

We prove analogs of Brooks' Theorem for the list-distinguishing chromatic number of different classes of simple finite connected graphs. Moreover, we determine two upper bounds for the list-distinguishing chromatic number of a graph G in…

We introduce remarkable upper bounds for the interpolation error constants on triangles, which are sharp and given by simple formulas. These constants are crucial in analyzing interpolation errors, particularly those associated with the…

We give an algorithm to compute a morph between any two convex drawings of the same plane graph. The morph preserves the convexity of the drawing at any time instant and moves each vertex along a piecewise linear curve with linear…

We show that $z\in\R^n$ is computably random if and only if every computable monotone function on $\R^n$ is differentiable at $z$.

Morphisms are homomorphisms under the concatenation operation of the set of words over a finite set. Changing the elements of the finite set does not essentially change the morphism. We propose a way to select a unique representing member…

A recent conjecture of Caputo, Carlen, Lieb, and Loss, and, independently, of the author, states that the maximum of the permanent of a matrix whose rows are unit vectors in l_p is attained either for the identity matrix I or for a constant…

Recognizable languages of finite words are part of every computer science cursus, and they are routinely described as a cornerstone for applications and for theory. We would like to briefly explore why that is, and how this word-related…

The relative fixity of a digraph $\Gamma$ is defined as the ratio between the largest number of vertices fixed by a nontrivial automorphism of $\Gamma$ and the number of vertices of $\Gamma$. We characterize the vertex-primitive digraphs…

A compact set has computable type if any homeomorphic copy of the set which is semicomputable is actually computable. Miller proved that finite-dimensional spheres have computable type, Iljazovi\'c and other authors established the property…

The computational complexity of the graph isomorphism problem is considered to be a major open problem in theoretical computer science. It is known that testing isomorphism of chordal graphs is polynomial-time equivalent to the general…

We give a short proof of the cross norm characterization of separability due to O. Rudolph and show how its computation, for a fixed chosen error, can be reduced to a linear programming problem whose dimension grows polynomially with the…