Related papers: Detecting properties from descriptions of groups

The main features of a family of efficient algorithms for recognition and classification of complex patterns are briefly reviewed. They are inspired in the observation that fast synaptic noise is essential for some of the processing of…

This study presents the approach to analyzing the evolution of an arbitrary complex system whose behavior is characterized by a set of different time-dependent factors. The key requirement for these factors is only that they must contain an…

Community detection is considered as a fundamental task in analyzing social networks. Even though many techniques have been proposed for community detection, most of them are based exclusively on the connectivity structures. However, there…

Different aspects of the predictability problem in dynamical systems are reviewed. The deep relation among Lyapunov exponents, Kolmogorov-Sinai entropy, Shannon entropy and algorithmic complexity is discussed. In particular, we emphasize…

We show how complexity theory can be introduced in machine learning to help bring together apparently disparate areas of current research. We show that this new approach requires less training data and is more generalizable as it shows…

In this work, we investigate the phenomenon that robust image classifiers have human-recognizable features -- often referred to as interpretability -- as revealed through the input gradients of their score functions and their subsequent…

Statistical significance of network clustering has been an unresolved problem since it was observed that community detection algorithms produce false positives even in random graphs. After a phase transition between undetectable and…

Group fairness, a class of fairness notions that measure how different groups of individuals are treated differently according to their protected attributes, has been shown to conflict with one another, often with a necessary cost in loss…

The community structure of a complex network can be determined by finding the partitioning of its nodes that maximizes modularity. Many of the proposed algorithms for doing this work by recursively bisecting the network. We show that this…

We present a new method for inferring complexity properties for a class of programs in the form of flowcharts annotated with loop information. Specifically, our method can (soundly and completely) decide if computed values are polynomially…

A coarse description of a subset A of omega is a subset D of omega such that the symmetric difference of A and D has asymptotic density 0. We study the extent to which noncomputable information can be effectively recovered from all coarse…

Consider pairs of the form (G, N), with G a group and N \normal G, as objects of a category \PG. A morphism (G_1, N_1) \To (G_2, N_2) will be a group homomorphism f : G_1 \To G_2 such that f(N_1) \subset N_2. We introduce a functor Q : \PG…

We investigate the computational complexity for determining various properties of a finite transformation semigroup given by generators. We introduce a simple framework to describe transformation semigroup properties that are decidable in…

The operationalization of algorithmic fairness comes with several practical challenges, not the least of which is the availability or reliability of protected attributes in datasets. In real-world contexts, practical and legal impediments…

We use rewriting systems to spell out cup-products in the (twisted) cohomology groups of a product of surface groups. This allows us to detect a non-trivial obstruction bounding from below the effective topological complexity of an…

A combinatorial property of prositive group presentations, called completeness, is introduced, with an effective criterion for recognizing complete presentations, and an iterative method for completing an incomplete presentation. We show…

We study the computational problem of rigorously describing the asymptotic behaviour of topological dynamical systems up to a finite but arbitrarily small pre-specified error. More precisely, we consider the limit set of a typical orbit,…

In this article we survey recent progress in the algorithmic theory of matrix semigroups. The main objective in this area of study is to construct algorithms that decide various properties of finitely generated subsemigroups of an infinite…

A method of random search based on Kolmogorov complexity is proposed and applied to two search problems in group theory. The method is provably effective but not practical, so the applications involve heuristic approximations. Perhaps…

This paper investigates some issues arising in categorical models of reversible logic and computation. Our claim is that the structural (coherence) isomorphisms of these categorical models, although generally overlooked, have decidedly…