Related papers: Complexity of matrix problems
In this paper, we study three matching problems all of which came up quite recently in the field of machine teaching. The cost of a matching is defined in such a way that, for some formal model of teaching, it equals (or bounds) the number…
We study the complexity of isomorphism problems for d-way arrays, or tensors, under natural actions by classical groups such as orthogonal, unitary, and symplectic groups. Such problems arise naturally in statistical data analysis and…
We investigate the $\mathcal F$-Borel complexity of topological spaces in their different compactifcations. We provide a simple proof of the fact that a space can have arbitrarily many different complexities in different compactifications.…
For certain problems involving vector fields, it is possible to find an associated imaginary field that, in conjunction with the first, forms a complex field for which the equation can be solved. This result is generalized to arbitrary…
Many fundamental questions in theoretical computer science are naturally expressed as special cases of the following problem: Let $G$ be a complex reductive group, let $V$ be a $G$-module, and let $v,w$ be elements of $V$. Determine if $w$…
The problem of classifying all unitary R-matrices of arbitrary finite dimension that have precisely two distinct eigenvalues is described, working up to a natural equivalence relation given by the characters of their braid group…
We consider optimization problems involving the multiplication of variable matrices to be selected from a given family, which might be a discrete set, a continuous set or a combination of both. Such nonlinear, and possibly discrete,…
An algorithm of solution of the Automatic Classification (AC for brevity) problem is set forth in the paper. In the AC problem, it is required to find one or several artitions, starting with the given pattern matrix or dissimilarity,…
We study the complexity of the classification problem for countable models of set theory (ZFC). We prove that the classification of arbitrary countable models of ZFC is Borel complete, meaning that it is as complex as it can conceivably be.…
The worst-case complexity of group-theoretic algorithms has been studied for a long time. Generic-case complexity, or complexity on random inputs, was introduced and studied relatively recently. In this paper, we address the average-case…
The study of complexity and optimization in decision theory involves both partial and complete characterizations of preferences over decision spaces in terms of real-valued monotones. With this motivation, and following the recent…
We study the expression complexity of two basic problems involving the comparison of primitive positive formulas: equivalence and containment. In particular, we study the complexity of these problems relative to finite relational…
A general problem in complex cobordism theory is to find useful representatives for cobordism classes. One particularly convenient class of complex manifolds consists of smooth projective toric varieties. The bijective correspondence…
A variety is a category of ordered (finitary) algebras presented by inequations between terms. We characterize categories enriched over the category of posets which are equivalent to a variety. This is quite analogous to Lawvere's classical…
We introduce the NP-complete problem 3SAT_N and extend Tovey's results to a classification theorem for this problem. This theorem leads us to generalize the concept of truth assignments for SAT to aggressive truth assignments for 3SAT_N. We…
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…
When filtering a topological space by a single parameter, the theory of quiver representations provides a complete framework for decomposing the resulting persistence module to obtain its barcode. This is achieved by interpreting the…
We prove that every finite dimensional algebra over an algebraically closed field is either derived tame or derived wild. The proof is based on the technique of matrix problems (boxes and reduction algorithm). It implies, in particular,…
We introduce the notion of (twisted) quiver representations in abelian categories and study the category of such representations. We construct standard resolutions and coresolutions of quiver representations and study basic homological…
In this paper we investigate the complexity of abduction, a fundamental and important form of non-monotonic reasoning. Given a knowledge base explaining the world's behavior it aims at finding an explanation for some observed manifestation.…