Related papers: The complexity of MinRank

Rank minimization is of interest in machine learning applications such as recommender systems and robust principal component analysis. Minimizing the convex relaxation to the rank minimization problem, the nuclear norm, is an effective…

We prove a very general lower bound technique for quantum and randomized query complexity, that is easy to prove as well as to apply. To achieve this, we introduce the use of Kolmogorov complexity to query complexity. Our technique…

Given the emergent reasoning abilities of large language models, information retrieval is becoming more complex. Rather than just retrieve a document, modern information retrieval systems advertise that they can synthesize an answer based…

We investigate a correspondence between the complexity hierarchy of constraint satisfaction problems and a hierarchy of logical compactness hypotheses for finite relational structures. It seems that the harder a constraint satisfaction…

We present connections between the recent literature on multigroup fairness for prediction algorithms and classical results in computational complexity. Multiaccurate predictors are correct in expectation on each member of an arbitrary…

We show that the Word Problem in finitely generated subgroups of $\textsf{GL}_d(\mathbb{Z})$ can be solved in linear average-case complexity. This is done under the bit-complexity model, which accounts for the fact that large integers are…

We develop a topological approach to prove the generalized Lax conjecture using the fact that determinants of sufficiently big symmetric linear pencils are able to express the rigidly convex sets of RZ polynomials of any degree $d$.…

We investigate the relationship between several enumeration complexity classes and focus in particular on problems having enumeration algorithms with incremental and polynomial delay (IncP and DelayP respectively). We show that, for some…

We consider sentence-definable and diagram-definable subfamilies of given families of theories, calculi for these subfamilies, as well dynamics and characteristics of these subfamilies with respect to rank and degree.

We first show that infinite satisfiability can be reduced to finite satisfiability for all prenex formulas of Separation Logic with $k\geq1$ selector fields ($\seplogk{k}$). Second, we show that this entails the decidability of the finite…

In this paper, we present a more complete version of the minimax theorem established in [7]. As a consequence, we get, for instance, the following result: Let $X$ be a compact, not singleton subset of a normed space $(E,\|\cdot\|)$ and let…

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…

We prove that the problem of determining whether a finite logical matrix determines an algebraizable logic is complete for EXPTIME. The same result holds for the classes of order algebraizable, weakly algebraizable, equivalential and…

Constant-recursive sequences are those which satisfy a linear recurrence, so that later terms can be obtained as a linear combination of the previous ones. The rank of a constant-recursive sequence is the minimal number of previous terms…

In model selection problems for machine learning, the desire for a well-performing model with meaningful structure is typically expressed through a regularized optimization problem. In many scenarios, however, the meaningful structure is…

This work generalizes the short resolution given in Proc. Amer. Math. Soc. \textbf{131}, 4, (2003), 1081--1091, to any affine semigroup. Moreover, a characterization of Ap\'{e}ry sets is given. This characterization lets compute Ap\'{e}ry…

The congested clique model of distributed computing has been receiving attention as a model for densely connected distributed systems. While there has been significant progress on the side of upper bounds, we have very little in terms of…

In this paper, we study a novel problem, Minimum Robust Multi-Submodular Cover for Fairness (MinRF), as follows: given a ground set $V$; $m$ monotone submodular functions $f_1,...,f_m$; $m$ thresholds $T_1,...,T_m$ and a non-negative…

We introduce constraints necessary for type checking a higher-order concurrent constraint language, and solve them with an incremental algorithm. Our constraint system extends rational unification by constraints x$\subseteq$ y saying that…

Frequent pattern mining is widely used to find ``important'' or ``interesting'' patterns in data. While it is not easy to mathematically define such patterns, maximal frequent patterns are promising candidates, as frequency is a natural…