Related papers: Testability in group theory
A property of finite graphs is called nondeterministically testable if it has a "certificate" such that once the certificate is specified, its correctness can be verified by random local testing. In this paper we study certificates that…
Satisfiability is a classic problem in computational complexity theory, in which one wishes to determine whether an assignment of values to a collection of Boolean variables exists in which all of a collection of clauses composed of logical…
We are interested in verifying dynamic properties of finite state reactive systems under fairness assumptions by model checking. The systems we want to verify are specified through a top-down refinement process. In order to deal with the…
In the paper we characterize the class of finite solvable groups by two-variable identities in a way similar to the characterization of finite nilpotent groups by Engel identities. More precisely, a sequence of words $u_1,...,u_n,... $ is…
We prove that the alternating group of a topologically free action of a countably infinite group $\Gamma$ on the Cantor set has the property that all of its $\ell^2$-Betti numbers vanish and, in the case that $\Gamma$ is amenable, is stable…
We outline a general procedure that builds classifying spaces for generalized Thompson groups $\Gamma$. The construction depends on a small number of choices: (1) an inverse semigroup $S$ of partial transformations that ``locally determine"…
We study the complexity of constraint satisfaction problems for templates $\Gamma$ that are first-order definable in $(\Bbb Z; succ)$, the integers with the successor relation. Assuming a widely believed conjecture from finite domain…
We give an affirmative answer to the Grunwald problem for new families of non-solvable finite groups G, away from the set of primes dividing |G|. Furthermore, we show that such G verify the condition (BM), that is, the Brauer-Manin…
The main problem in the area of graph property testing is to understand which graph properties are \emph{testable}, which means that with constantly many queries to any input graph $G$, a tester can decide with good probability whether $G$…
The group isomorphism problem in computational complexity asks whether two finite groups given by their Cayley tables are isomorphic or not. Although polynomial-time isomorphism tests exist for many specific types of groups, no general…
Let $X$ be a set and let $S$ be an inverse semigroup of partial bijections of $X$. Thus, an element of $S$ is a bijection between two subsets of $X$, and the set $S$ is required to be closed under the operations of taking inverses and…
Permutation tests date back nearly a century to Fisher's randomized experiments, and remain an immensely popular statistical tool, used for testing hypotheses of independence between variables and other common inferential questions. Much of…
Non-adaptive group testing involves grouping arbitrary subsets of $n$ items into different pools. Each pool is then tested and defective items are identified. A fundamental question involves minimizing the number of pools required to…
We consider the sequential composite binary hypothesis testing problem in which one of the hypotheses is governed by a single distribution while the other is governed by a family of distributions whose parameters belong to a known set…
In this paper we criticize the robustness measure traditionally employed to assess the performance of machine learning models deployed in adversarial settings. To mitigate the limitations of robustness, we introduce a new measure called…
We investigate the flat holomorphic vector bundles over compact complex parallelizable manifolds $G / \Gamma$, where $G$ is a complex connected Lie group and $\Gamma$ is a cocompact lattice in it. The main result proved here is a structure…
Informed by our understanding of the tt-geometry of permutation modules, we investigate the proper definition of the `stable permutation category' of a finite group. Then we prove that this category decomposes over cyclic and generalized…
In this paper we study a new, generalized version of the well-known group testing problem. In the classical model of group testing we are given n objects, some of which are considered to be defective. We can test certain subsets of the…
The title refers to the area of research which studies infinite groups using measure-theoretic tools, and studies the restrictions that group structure imposes on ergodic theory of their actions. The paper is a survey of recent developments…
We investigate fixed-point properties of automorphisms of groups similar to R. Thompson's group $F$. Revisiting work of Gon\c{c}alves-Kochloukova, we deduce a cohomological criterion to detect infinite fixed-point sets in the…