Related papers: Ranking Functions for Linear-Constraint Loops
We consider a class of optimization problems that involve determining the maximum value that a function in a particular class can attain subject to a collection of difference constraints. We show that a particular linear programming…
Determining whether a given program terminates is the quintessential undecidable problem. Algorithms for termination analysis are divided into two groups: (1) algorithms with strong behavioral guarantees that work in limited circumstances…
A common problem in machine learning is to rank a set of n items based on pairwise comparisons. Here ranking refers to partitioning the items into sets of pre-specified sizes according to their scores, which includes identification of the…
A rational approximation by a ratio of polynomial functions is a flexible alternative to polynomial approximation. In particular, rational functions exhibit accurate estimations to nonsmooth and non- Lipschitz functions, where polynomial…
We consider the following problem: given a program, find tight asymptotic bounds on the values of some variables at the end of the computation (or at any given program point) in terms of its input values. We focus on the case of…
We study the algorithmic complexity of the problem of deciding whether a Linear Time Invariant dynamical system with rational coefficients has bounded trajectories. Despite its ubiquitous and elementary nature in Systems and Control, it…
We address the problem of testing weak optimality of a given solution of a given interval linear program. The problem was recently wrongly stated to be polynomially solvable. We disprove it. We show that the problem is NP-hard in general.…
Here we study the computational complexity of the constrained synchronization problem for the class of regular commutative constraint languages. Utilizing a vector representation of regular commutative constraint languages, we give a full…
We show factorization of polynomials in one variable over the tropical semiring is in general NP-complete, either if all coefficients are finite, or if all are either 0 or infinity (Boolean case). We give algorithms for the factorization…
We classify, according to their computational complexity, integer optimization problems whose constraints and objective functions are polynomials with integer coefficients and the number of variables is fixed. For the optimization of an…
We present new deterministic algorithms for several cases of the maximum rank matrix completion problem (for short matrix completion), i.e. the problem of assigning values to the variables in a given symbolic matrix as to maximize the…
Learning-to-rank techniques have proven to be extremely useful for prioritization problems, where we rank items in order of their estimated probabilities, and dedicate our limited resources to the top-ranked items. This work exposes a…
Motivated by the search for a logic for polynomial time, we study rank logic (FPR) which extends fixed-point logic with counting (FPC) by operators that determine the rank of matrices over finite fields. While FPR can express most of the…
We investigate the termination problem of a family of multi-path polynomial programs (MPPs), in which all assignments to program variables are polynomials, and test conditions of loops and conditional statements are polynomial equalities.…
We propose an extension of the framework for discussing the computational complexity of problems involving uncountably many objects, such as real numbers, sets and functions, that can be represented only through approximation. The key idea…
In this paper, we study the general problem of optimizing a convex function $F(L)$ over the set of $p \times p$ matrices, subject to rank constraints on $L$. However, existing first-order methods for solving such problems either are too…
We investigate infinitary wellfounded systems for linear logic with fixed points, with transfinite branching rules indexed by some closure ordinal $\alpha$ for fixed points. Our main result is that provability in the system for some…
We study the program complexity of datalog on both finite and infinite linear orders. Our main result states that on all linear orders with at least two elements, the nonemptiness problem for datalog is EXPTIME-complete. While containment…
This is the latest in a series of articles aimed at exploring the relationship between the complexity classes of P and NP. In the previous papers, we have proved that the sat CNF problem is polynomially reduced to the problem of finding a…
In most machine learning applications, classification accuracy is not the primary metric of interest. Binary classifiers which face class imbalance are often evaluated by the $F_\beta$ score, area under the precision-recall curve, Precision…