Research
Research
Research
Research
3,812+ open-access research outputs.
We prove superpolynomial length lower bounds for the semantic tree-like Frege refutation system with bounded line size. Concretely, for any function $n^{2-\varepsilon} \leq s(n) \leq 2^{n^{1-\varepsil…
In this paper, we consider the Santa Claus problem in the CONGEST model. This NP-hard problem can be modeled as a bipartite graph of children and gifts where an edge indicates that a child desires a g…
An important tool in the design of fault-tolerant graph data structures are $(L,f)$-replacement path coverings (RPCs). An RPC is a family $\mathcal{G}$ of subgraphs of a given graph $G$ such that, for…
We study when a sound arithmetic theory $\mathcal S{\supseteq}S^1_2$ with polynomial-time decidable axioms efficiently proves the bounded consistency statements $Con_{\mathcal S{+}\phi}(n)$ for a true…
We develop a geometric and information-theoretic framework for encoder-decoder learning built on the Information Bottleneck (IB) principle. Recasting IB as a rate-distortion problem with Kullback-Leib…
Large Language Models (LLMs) have been widely applied to student-facing educational tools, this work explores their use in supporting instructors by presenting a practical adaptation of the Framework …
This study examines the development, influence, and collaboration patterns in AI-supported social presence research within online learning environments. Utilizing 59 open-access empirical studies from…
Distributional learning provides a framework for studying the learnability of structured languages from positive data. In this paper, we extend this framework to graph languages generated by fixed-int…
In this work we contribute to the study of the fine-grained complexity of problems parameterized by multi-clique-width, which was initiated by F\"urer [ITCS 2017] and pursued further by Chekan and Kra…
In the context of quantum secure scenarios, existing research on mobile edge devices and intelligent computing and edge (ICE) systems based on the Non-Orthogonal Multiple Access (NOMA) communication m…
We study the rainbow matching (RM) problem: given an edge-colored graph, find a maximum matching with at most one edge of each color. Rainbow matchings correspond to stable sets in the \emph{augmented…
In this paper, we investigate the problem of designing $(n, N; \mathcal{B})$-reconstruction codes for $N\in \{14,11,9,5\}$, where $\mathcal{B}$ is the single-deletion single-substitution ball function…
This paper uncovers an exact $\chi^2$ dissipation identity for the Blahut--Arimoto (BA) flow and establishes its fundamental information-geometric structure. While prior works have analyzed BA converg…
Information theory is a powerful framework to capture aspects of dynamical systems with multiple degrees of freedom. Mathematically, the dynamics can be represented as a continuous curve $\mathcal{C}$…
Motivated by the FPTAS for connectivity interdiction of Huang et al. (IPCO'24), we isolate the part of the argument that does not use cuts. The setting is a minimization problem over a feasible-set fa…
We study the common intersection of arrangements of double-wedges. We consider arrangements where double-wedges may be either bowties (which do not contain a vertical line) or hourglasses (which conta…
Motivated by entanglement-assisted quantum error-correcting codes, where the hull dimension determines the number of required pre-shared entangled pairs, we study hulls of two families of $\mathbb{F}_…
The first-order (FO) model checking problem asks, given an FO sentence $\phi$ and a graph $G$, whether $G$ is a model of $\phi$. This problem is known to be $\mathsf{AW[*]}$-hard when parameterized by…
Education is not merely the transmission of information or the optimisation of individual performance; it is a fundamentally social, constructive, and relational practice. However, recent advances in …
Capacitated Vertex Cover is the hard-capacitated variant of Vertex Cover: given a graph, a capacity for every vertex, and an integer $k$, the task is to select at most $k$ vertices that cover all edge…
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