Related papers: On the distributed evaluation of recursive queries…

Verifying graph algorithms has long been considered challenging in separation logic, mainly due to structural sharing between graph subcomponents. We show that these challenges can be effectively addressed by representing graphs as a…

In this work we introduce a new notion: local mechanisms. These are truthful mechanisms that have an implementation as fast distributed algorithms and non-trivial approximation guarantees. We show how monotone distributed optimisation…

We study the first-order (FO) model checking problem of dense graphs, namely those which have FO interpretations in (or are FO transductions of) some sparse graph classes. We give a structural characterization of the graph classes which are…

Various feature descriptions are being employed in logic programming languages and constrained-based grammar formalisms. The common notational primitive of these descriptions are functional attributes called features. The descriptions…

We establish the equivalence between a class of asynchronous distributed automata and a small fragment of least fixpoint logic, when restricted to finite directed graphs. More specifically, the logic we consider is (a variant of) the…

In pioneering work from 2019, Barcel\'o and coauthors identified logics that precisely match the expressive power of constant iteration-depth graph neural networks (GNNs) relative to properties definable in first-order logic. In this…

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…

First-order linear temporal logic (FOLTL) is a flexible and expressive formalism capable of naturally describing complex behaviors and properties. Although the logic is in general highly undecidable, the idea of using it as a specification…

Motivated by the increasing need to understand the distributed algorithmic foundations of large-scale graph computations, we study some fundamental graph problems in a message-passing model for distributed computing where $k \geq 2$…

We present a new flow framework for separation logic reasoning about programs that manipulate general graphs. The framework overcomes problems in earlier developments: it is based on standard fixed point theory, guarantees least flows,…

We develop the first two heap logics that have implicit heaplets and that admit FO-complete program verification. The notion of FO-completeness is a theoretical guarantee that all theorems that are valid when recursive definitions are…

Functional graphs (FGs) model the graph structures used to analyse the behaviour of functions from a discrete set to itself. In turn, such functions are used to study real complex phenomena evolving in time. As the systems involved can be…

We study the expressive power of message-passing aggregate-combine-readout graph neural networks (ACR-GNNs). Particularly, we focus on the first-order (FO) properties expressible by this formalism. While a tight logical characterisation…

This paper is centered on the complexity of graph problems in the well-studied LOCAL model of distributed computing, introduced by Linial [FOCS '87]. It is widely known that for many of the classic distributed graph problems (including…

In this work, we present a fast distributed algorithm for local potential problems: these are graph problems where the task is to find a locally optimal solution where no node can unilaterally improve the utility in its local neighborhood…

Frick and Grohe [J. ACM 48 (2006), 1184-1206] introduced a notion of graph classes with locally bounded tree-width and established that every first order logic property can be decided in almost linear time in such a graph class. Here, we…

This paper presents the first use of graph neural networks (GNNs) for higher-order proof search and demonstrates that GNNs can improve upon state-of-the-art results in this domain. Interactive, higher-order theorem provers allow for the…

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-interface clause systems. We formulate…

This paper presents matching logic, a first-order logic (FOL) variant for specifying and reasoning about structure by means of patterns and pattern matching. Its sentences, the patterns, are constructed using variables, symbols, connectives…

This paper presents a distributed agent-based automated theorem proving framework based on order-sorted first-order logic. Each agent in our framework has its own knowledge base, communicating to its neighboring agent(s) using…