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The Boolean satisfiability problem (SAT) is a well-known example of monotonic reasoning, of intense practical interest due to fast solvers, complemented by rigorous fine-grained complexity results. However, for non-monotonic reasoning,…
We bring forward a logical system of transition algebras that enhances many-sorted first-order logic using features from dynamic logics. The sentences we consider include compositions, unions, and transitive closures of transition…
We study the conditions under which the convex relaxation of a mixed-integer linear programming formulation for ordered optimization problems, where sorting is part of the decision process, yields integral optimal solutions. Thereby solving…
The theory of optimal choice sets offers a well-established solution framework in social choice and game theory. In social choice theory, decision-making is typically modeled as a maximization problem. However, when preferences are cyclic…
We extend classical methods of computational complexity to the realm of distributed computing, where they sometimes prove more effective than in their original context. Our focus is on decision problems in the LOCAL model, a setting in…
This work investigates the algorithmic complexity of non-classical logics, focusing on superintuitionistic and modal systems. It is shown that propositional logics are usually polynomial-time reducible to their fragments with at most two…
We study the stable marriage problem in the partial information setting where the agents, although they have an underlying true strict linear order, are allowed to specify partial orders. Specifically, we focus on the case where the agents…
An instance $I$ of the Stable Matching Problem (SMP) is given by a bipartite graph with a preference list of neighbors for every vertex. A swap in $I$ is the exchange of two consecutive vertices in a preference list. A swap can be viewed as…
Variational analysis provides the theoretical foundations and practical tools for constructing optimization algorithms without being restricted to smooth or convex problems. We survey the central concepts in the context of a concrete but…
In this work, we propose a novel formulation for the solution of partial differential equations using finite element methods on unfitted meshes. The proposed formulation relies on the discrete extension operator proposed in the aggregated…
This is the second in a series of articles aimed at exploring the relationship between the complexity classes of P and NP. The research in this article aims to find conditions of an algorithmic nature that are necessary and sufficient to…
Interpretability methods are valuable only if their explanations faithfully describe the explained model. In this work, we consider neural networks whose predictions are invariant under a specific symmetry group. This includes popular…
We consider the problem of testing whether the points in a complex or real variety with non-zero coordinates form a multiplicative group or, more generally, a coset of a multiplicative group. For the coset case, we study the notion of…
Indirect reciprocity is a key explanation for the exceptional magnitude of cooperation among humans. This literature suggests that a large proportion of human cooperation is driven by social norms and individuals' incentives to maintain a…
Variable viscosity arises in many flow scenarios, often imposing numerical challenges. Yet, discretisation methods designed specifically for non-constant viscosity are few, and their analysis is even scarcer. In finite element methods for…
Robustness is a property of system analyses, namely monotonic maps from the complete lattice of subsets of a (system's state) space to the two-point lattice. The definition of robustness requires the space to be a metric space. Robust…
We argue that robustness of explanations---i.e., that similar inputs should give rise to similar explanations---is a key desideratum for interpretability. We introduce metrics to quantify robustness and demonstrate that current methods do…
We propose an Extended Hybrid High-Order scheme for the Poisson problem with solution possessing weak singularities. Some general assumptions are stated on the nature of this singularity and the remaining part of the solution. The method is…
Non-probability samples become increasingly popular in survey statistics but may suffer from selection biases that limit the generalizability of results to the target population. We consider integrating a non-probability sample with a…
Machine learning methods have significantly improved in their predictive capabilities, but at the same time they are becoming more complex and less transparent. As a result, explainers are often relied on to provide interpretability to…