Related papers: Locally Checkable Labelings with Small Messages

In-context Learning (ICL) has emerged as a powerful capability alongside the development of scaled-up large language models (LLMs). By instructing LLMs using few-shot demonstrative examples, ICL enables them to perform a wide range of tasks…

Many combinatorial optimization problems can be approximated within $(1 \pm \epsilon)$ factors in $\text{poly}(\log n, 1/\epsilon)$ rounds in the LOCAL model via network decompositions [Ghaffari, Kuhn, and Maus, STOC 2018]. These approaches…

The Local Learning Coefficient (LLC) is introduced as a novel complexity measure for deep neural networks (DNNs). Recognizing the limitations of traditional complexity measures, the LLC leverages Singular Learning Theory (SLT), which has…

Graph clustering is a fundamental problem that has been extensively studied both in theory and practice. The problem has been defined in several ways in literature and most of them have been proven to be NP-Hard. Due to their high practical…

We study the possibility of designing $N^{o(1)}$-round protocols for problems of substantially super-linear polynomial-time (sequential) complexity on the congested clique with about $N^{1/2}$ nodes, where $N$ is the input size. We show…

We introduce a family of balanced locally repairable codes (BLRCs) $[n, k, d]$ for arbitrary values of $n$, $k$ and $d$. Similar to other locally repairable codes (LRCs), the presented codes are suitable for applications that require a low…

This paper investigates properties of realizations of linear or group codes on general graphs that lead to local reducibility. Trimness and properness are dual properties of constraint codes. A linear or group realization with a constraint…

We completely classify the computational complexity of the list H-colouring problem for graphs (with possible loops) in combinatorial and algebraic terms: for every graph H the problem is either NP-complete, NL-complete, L-complete or is…

Consider a distributed task where the communication network is fixed but the local inputs given to the nodes of the distributed system may change over time. In this work, we explore the following question: if some of the local inputs…

A locally correctable code (LCC) is an error correcting code that allows correction of any arbitrary coordinate of a corrupted codeword by querying only a few coordinates. We show that any {\em zero-error} $2$-query locally correctable code…

In this work, we study the problem of computing a maximum common contraction of two vertex-labeled graphs, i.e. how to make them identical by contracting as little edges as possible in the two graphs. We study the problem from a…

We show that any one-round algorithm that computes a minimum spanning tree (MST) in the unicast congested clique must use a link bandwidth of $\Omega(\log^3 n)$ bits in the worst case. Consequently, computing an MST under the standard…

Bonne and Censor-Hillel (ICALP 2019) initiated the study of distributed subgraph finding in dynamic networks of limited bandwidth. For the case where the target subgraph is a clique, they determined the tight bandwidth complexity bounds in…

Local Completeness Logic (LCL) has been put forward as a program logic for proving both the correctness and incorrectness of program specifications. LCL is an abstract logic, parameterized by an abstract domain that allows combining over-…

We study connections between distributed local algorithms, finitary factors of iid processes, and descriptive combinatorics in the context of regular trees. We extend the Borel determinacy technique of Marks coming from descriptive…

Effective light cones, characterized by Lieb-Robinson bounds, emerge in nonrelativistic local quantum systems. Here, we present several analytical results derived from logarithmic light cones (LLCs). Possible origins of LLCs include the…

Qualitative data analysis provides insight into the underlying perceptions and experiences within unstructured data. However, the time-consuming nature of the coding process, especially for larger datasets, calls for innovative approaches,…

We classify the complexity of the LTL satisfiability and model checking problems for several standard parameterisations. The investigated parameters are temporal depth, number of propositional variables and formula treewidth, resp.,…

The theory of asymptotic complexity provides an approach to characterizing the behavior of programs in terms of bounds on the number of computational steps executed or use of computational resources. We describe work using ACL2 to prove…

We consider the problem of bounded model checking (BMC) for linear temporal logic (LTL). We present several efficient encodings that have size linear in the bound. Furthermore, we show how the encodings can be extended to LTL with past…