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We give a language-parametric solution to the problem of total correctness, by automatically reducing it to the problem of partial correctness, under the assumption that an expression whose value decreases with each program step in a…
Reasoning under uncertainty is a fundamental challenge in Artificial Intelligence. As with most of these challenges, there is a harsh dilemma between the expressive power of the language used, and the tractability of the computational…
The proportional fair resource allocation problem is a major problem studied in flow control of networks, operations research, and economic theory, where it has found numerous applications. This problem, defined as the constrained…
Complex logical reasoning tasks require a long sequence of reasoning, which a large language model (LLM) with chain-of-thought prompting still falls short. To alleviate this issue, neurosymbolic approaches incorporate a symbolic solver.…
We consider two formulations of the random-link fractional matching problem, a relaxed version of the more standard random-link (integer) matching problem. In one formulation, we allow each node to be linked to itself in the optimal…
We present a number of results concerning infinite-exponent partition relations on linear orders of the form $\langle {}^\alpha 2,<_{\text{lex}}\rangle$ for $\alpha$ an ordinal, generalising the setting of the real line, working throughout…
Let N be a square-free positive integer and let f be a newform of weight 2 on \Gamma_0(N). Let A denote the abelian subvariety of J_0(N) associated to f and let m be a maximal ideal of the Hecke algebra T that contains Ann_T(f) and has…
In this paper we study the problem of deciding whether two disjoint semialgebraic sets of an algebraic variety over R are separable by a polynomial. For that we isolate a dense subfamily of Spaces of Orderings, named Geometric, which…
We study two fundamental problems in communication, Document Exchange (DE) and Error Correcting Code (ECC). In the first problem, two parties hold two strings, and one party tries to learn the other party's string through communication. In…
We outline a recently developed theory of impedance-matching, or reflectionless excitation of arbitrary finite photonic structures in any dimension. It describes the necessary and sufficient conditions for perfectly reflectionless…
We study several variants of decomposing a symmetric matrix into a sum of a low-rank positive semidefinite matrix and a diagonal matrix. Such decompositions have applications in factor analysis and they have been studied for many decades.…
We study bounded deviation of non-deterministic finite transducers under the Hamming distance: the bounded comparison problem asks, given two transducers and $k \in \mathbb{N}$, whether for every input the two transducers produce words at…
Multi-relational learning has received lots of attention from researchers in various research communities. Most existing methods either suffer from superlinear per-iteration cost, or are sensitive to the given ranks. To address both issues,…
Separation is a classical problem in mathematics and computer science. It asks whether, given two sets belonging to some class, it is possible to separate them by another set of a smaller class. We present and discuss the separation problem…
In this paper, we present a new algorithm for computing the linear recurrence relations of multi-dimensional sequences. Existing algorithms for computing these relations arise in computational algebra and include constructing structured…
The (matricial) solution set of a Linear Matrix Inequality (LMI) is a convex basic non-commutative semi-algebraic set. The main theorem of this paper is a converse, a result which has implications for both semidefinite programming and…
Robust optimization is a framework for modeling optimization problems involving data uncertainty and during the last decades has been an area of active research. If we focus on linear programming (LP) problems with i) uncertain data, ii)…
Second-order conic optimization (SOCO) can be considered as a special case of semidefinite optimization (SDO). In the literature it has been advised that a SOCO problem can be embedded in an SDO problem using the arrow-head matrix…
Representing the semantic relations that exist between two given words (or entities) is an important first step in a wide-range of NLP applications such as analogical reasoning, knowledge base completion and relational information…
Let $\overline{p}_o(n)$ denote the number of overpartitions of $n$ into odd parts. The partition function $\overline{p}_o(n)$ has been the subject of many recent studies where many explicit Ramanujan-like congruences were discovered. In…