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In this paper we present the formal, computer-supported verification of a functional implementation of Buchberger's critical-pair/completion algorithm for computing Gr\"obner bases in reduction rings. We describe how the algorithm can be…
In this work, we revisit the problem of uniformity testing of discrete probability distributions. A fundamental problem in distribution testing, testing uniformity over a known domain has been addressed over a significant line of works, and…
While traditional Deep Learning (DL) optimization methods treat all training samples equally, Distributionally Robust Optimization (DRO) adaptively assigns importance weights to different samples. However, a significant gap exists between…
In a recent volume of Mathematics Magazine (Vol. 90, No. 3, June 2017) there is an interesting article by Seth Zimmerman, titled Detecting Deficiencies: An Optimal Group Testing Algorithm. The claim in the summary is contradictory to…
We describe a Lohner-type algorithm for the computation of rigorous upper bounds for reachable set for control systems, solutions of ordinary differential inclusions and perturbations of ODEs.
The Chinese Remainder Theorem for the integers says that every system of congruence equations is solvable as long as the system satisfies an obvious necessary condition. This statement can be generalized in a natural way to arbitrary…
A general primal-dual splitting algorithm for solving systems of structured coupled monotone inclusions in Hilbert spaces is introduced and its asymptotic behavior is analyzed. Each inclusion in the primal system features compositions with…
Estimating the ratio of two probability densities from finitely many samples, is a central task in machine learning and statistics. In this work, we show that a large class of kernel methods for density ratio estimation suffers from error…
In this paper, we study the strong convergence of an algorithm to solve the variational inequality problem which extends(Thong et al, Numerical Algorithms. 78, 1045-1060 (2018)). We have reduced and refined some of their algorithm's…
Calculi with control operators have been studied as extensions of simple type theory. Real programming languages contain datatypes, so to really understand control operators, one should also include these in the calculus. As a first step in…
We describe a simple algorithm which, for a given D0L system, returns all factors $v$ such that $v^k$ is in the language of the system for all $k$. This algorithm can be used to decide whether a D0L system is repetitive.
We introduce a new -as far as we know- problem, according to which we are asked to match sequences of two digits in matrices having entries among those two digits (but others too) and prove that this problem is NP-complete
Recursive algebraic data types (term algebras, ADTs) are one of the most well-studied theories in logic, and find application in contexts including functional programming, modelling languages, proof assistants, and verification. At this…
Bidirectional typing is a discipline in which the typing judgment is decomposed explicitly into inference and checking modes, allowing to control the flow of type information in typing rules and to specify algorithmically how they should be…
In this paper, we introduce the concept of inner derivations of low-dimensional Zinbiel algebras and investigate their properties. The primary objective of this study is to develop an algorithm to characterize the inner derivations of any…
The extension of classical online algorithms when provided with predictions is a new and active research area. In this paper, we extend the primal-dual method for online algorithms in order to incorporate predictions that advise the online…
The definitional equality of an intensional type theory is its test of type compatibility. Today's systems rely on ordinary evaluation semantics to compare expressions in types, frustrating users with type errors arising when evaluation…
Testing deep learning-based systems is crucial but challenging due to the required time and labor for labeling collected raw data. To alleviate the labeling effort, multiple test selection methods have been proposed where only a subset of…
We sketch a tentative proof of P-completeness for the $\beta$-convertibility problem on untyped planar (a.k.a. ordered or non-commutative) $\lambda$-terms.
The authors' ATR programming formalism is a version of call-by-value PCF under a complexity-theoretically motivated type system. ATR programs run in type-2 polynomial-time and all standard type-2 basic feasible functionals are ATR-definable…