Related papers: On the distributed evaluation of recursive queries…

We study on which classes of graphs first-order logic (FO) and monadic second-order logic (MSO) have the same expressive power. We show that for all classes C of graphs that are closed under taking subgraphs, FO and MSO have the same…

We study first-order logic over unordered structures whose elements carry a finite number of data values from an infinite domain. Data values can be compared wrt.\ equality. As the satisfiability problem for this logic is undecidable in…

Model checking linear-time properties expressed in first-order logic has non-elementary complexity, and thus various restricted logical languages are employed. In this paper we consider two such restricted specification logics, linear…

Order-invariant formulas access an ordering on a structure's universe, but the model relation is independent of the used ordering. Order invariance is frequently used for logic-based approaches in computer science. Order-invariant formulas…

Kuske and Schweikardt introduced the very expressive first-order counting logic FOC(P) to model database queries with counting operations. They showed that there is an efficient model-checking algorithm on graphs with bounded degree, while…

This article describes a very high-level language for clear description of distributed algorithms and optimizations necessary for generating efficient implementations. The language supports high-level control flows where complex…

A central theme in distributed network algorithms concerns understanding and coping with the issue of locality. Inspired by sequential complexity theory, we focus on a complexity theory for distributed decision problems. In the context of…

We considers how a particular kind of graph corresponds to multiplicative intuitionistic linear logic formula. The main feature of the graphical notation is that it absorbs certain symmetries between conjunction and implication. We look at…

Proofs are traditionally syntactic, inductively generated objects. This paper reformulates first-order logic (predicate calculus) with proofs which are graph-theoretic rather than syntactic. It defines a combinatorial proof of a formula…

We consider graph properties that can be checked from labels, i.e., bit sequences, of logarithmic length attached to vertices. We prove that there exists such a labeling for checking a first-order formula with free set variables in the…

We investigate some basic questions about the interaction of regular and rational relations on words. The primary motivation comes from the study of logics for querying graph topology, which have recently found numerous applications. Such…

We study the design of graph filters to implement arbitrary linear transformations between graph signals. Graph filters can be represented by matrix polynomials of the graph-shift operator, which captures the structure of the graph and is…

The presence of embedded electronics and communication capabilities as well as sensing and control in smart devices has given rise to the novel concept of cyber-physical networks, in which agents aim at cooperatively solving complex tasks…

We demonstrate a deep learning framework which is inherently based in the highly expressive language of relational logic, enabling to, among other things, capture arbitrarily complex graph structures. We show how Graph Neural Networks and…

We propose a new formalism for specifying and reasoning about problems that involve heterogeneous "pieces of information" -- large collections of data, decision procedures of any kind and complexity and connections between them. The essence…

Well-founded fixed points have been used in several areas of knowledge representation and reasoning and to give semantics to logic programs involving negation. They are an important ingredient of approximation fixed point theory. We study…

Flow networks have attracted a lot of research in computer science. Indeed, many questions in numerous application areas can be reduced to questions about flow networks. Many of these applications would benefit from a framework in which one…

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

In this paper, we study distributed graph algorithms in networks in which the nodes have a limited communication capacity. Many distributed systems are built on top of an underlying networking infrastructure, for example by using a virtual…

We consider weighted structures, which extend ordinary relational structures by assigning weights, i.e. elements from a particular group or ring, to tuples present in the structure. We introduce an extension of first-order logic that allows…