Related papers: What can be certified compactly?

Graph and network visualization supports exploration, analysis and communication of relational data arising in many domains: from biological and social networks, to transportation and powergrid systems. With the arrival of AI-based…

The growing utilization of planning tools in practical scenarios has sparked an interest in generating multiple high-quality plans. Consequently, a range of computational problems under the general umbrella of top-quality planning were…

A locally testable language L is a language with the property that for some non negative integer k, called the order of local testability, whether or not a word u is in the language L depends on (1) the prefix and suffix of the word u of…

Locality is a fundamental principle used extensively in program and system optimization. It can be measured in many ways. This paper formalizes the metrics of locality into a measurement theory. The new theory includes the precise…

Inspired by branch-and-bound and cutting plane proofs in mixed-integer optimization and proof complexity, we develop a general approach via Hoffman's Helly systems. This helps to distill the main ideas behind optimality and infeasibility…

In this work we study the cost of local and global proofs on distributed verification. In this setting the nodes of a distributed system are provided with a nondeterministic proof for the correctness of the state of the system, and the…

We propose a simple and efficient local algorithm for graph isomorphism which succeeds for a large class of sparse graphs. This algorithm produces a low-depth canonical labeling, which is a labeling of the vertices of the graph that…

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…

We investigate certified robustness for GNNs under graph injection attacks. Existing research only provides sample-wise certificates by verifying each node independently, leading to very limited certifying performance. In this paper, we…

In this paper, we study the problem of certifying whether a graph is bipartite (i.e. $2$-colorable) with a locally checkable proof (LCP) that is able to hide a $2$-coloring from the verifier. More precisely, we say an LCP for $2$-coloring…

This paper presents a unified analysis framework that captures recent advances in the study of local-optimality characterizations for codes on graphs. These local-optimality characterizations are based on combinatorial structures embedded…

Common definitions of the "standard" LOCAL model tend to be sloppy and even self-contradictory on one point: do the nodes update their state using an arbitrary function or a computable function? So far, this distinction has been safe to…

A Locally Checkable Labeling (LCL) is a specification describing a set of labels that are valid with respect to a set of conditions that characterize a local part of a solution to a global problem. Conditions can only refer to nodes and…

In this work we introduce the graph-theoretic notion of mendability: for each locally checkable graph problem we can define its mending radius, which captures the idea of how far one needs to modify a partial solution in order to "patch a…

A number of recent papers -- e.g. Brandt et al. (STOC 2016), Chang et al. (FOCS 2016), Ghaffari & Su (SODA 2017), Brandt et al. (PODC 2017), and Chang & Pettie (FOCS 2017) -- have advanced our understanding of one of the most fundamental…

Modeling distributed computing in a way enabling the use of formal methods is a challenge that has been approached from different angles, among which two techniques emerged at the turn of the century: protocol complexes, and directed…

Network traffic analysis increasingly relies on feature-based representations to support monitoring and security in the presence of pervasive encryption. Although features are more compact than raw packet traces, their storage has become a…

ML models are typically trained using large datasets of high quality. However, training datasets often contain inconsistent or incomplete data. To tackle this issue, one solution is to develop algorithms that can check whether a prediction…

Certifying the robustness of a graph-based machine learning model poses a critical challenge for safety. Current robustness certificates for graph classifiers guarantee output invariance with respect to the total number of node pair flips…

Model checking large networks of processes is challenging due to state explosion. In many cases, individual processes are isomorphic, but there is insufficient global symmetry to simplify model checking. This work considers the verification…