Related papers: Slicewise definability in first-order logic with b…
First-order logic (FO) can express many algorithmic problems on graphs, such as the independent set and dominating set problem, parameterized by solution size. On the other hand, FO cannot express the very simple algorithmic question of…
We say that a first order sentence A defines a graph G if A is true on G but false on any graph non-isomorphic to G. Let L(G) (resp. D(G)) denote the minimum length (resp. quantifier rank) of a such sentence. We define the succinctness…
We study property testing of properties that are definable in first-order logic (FO) in the bounded-degree graph and relational structure models. We show that any FO property that is defined by a formula with quantifier prefix…
The focus of this paper is two fold. Firstly, we present a logical approach to graph modification problems such as minimum node deletion, edge deletion, edge augmentation problems by expressing them as an expression in first order (FO)…
We consider the problems of deciding whether an input graph can be modified by removing/adding at most k vertices/edges such that the result of the modification satisfies some property definable in first-order logic. We establish a number…
Logical formalisms such as first-order logic (FO) and fixpoint logic (FP) are well suited to express in a declarative manner fundamental graph functionalities required in distributed systems. We show that these logics constitute good…
It is known that first-order logic with some counting extensions can be efficiently evaluated on graph classes with bounded expansion, where depth-$r$ minors have constant density. More precisely, the formulas are $\exists x_1 ... x_k \#y…
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 the quantifier rank of the formula. A…
We contribute to the refined understanding of the language-logic-algebra interplay in the context of first-order properties of countable words. We establish decidable algebraic characterizations of one variable fragment of FO as well as…
We study property testing of properties that are definable in first-order logic (FO) in the bounded-degree graph and relational structure models. We show that any FO property that is defined by a formula with quantifier prefix…
We study first-order model checking, by which we refer to the problem of deciding whether or not a given first-order sentence is satisfied by a given finite structure. In particular, we aim to understand on which sets of sentences this…
Given a graph $F$, let $I(F)$ be the class of graphs containing $F$ as an induced subgraph. Let $W[F]$ denote the minimum $k$ such that $I(F)$ is definable in $k$-variable first-order logic. The recognition problem of $I(F)$, known as…
Graph Neural Networks (GNNs) address two key challenges in applying deep learning to graph-structured data: they handle varying size input graphs and ensure invariance under graph isomorphism. While GNNs have demonstrated broad…
We present a linear-time algorithm for deciding first-order (FO) properties in classes of graphs with bounded expansion, a notion recently introduced by Nesetril and Ossona de Mendez. This generalizes several results from the literature,…
For a sequence of random structures with $n$-element domains over a relational signature, we define its first order (FO) complexity as a certain subset in the Banach space $\ell^{\infty}/c_0$. The well-known FO zero-one law and FO…
We study various aspects of the first-order transduction quasi-order on graph classes, which provides a way of measuring the relative complexity of graph classes based on whether one can encode the other using a formula of first-order (FO)…
Let $F$ be a connected graph with $\ell$ vertices. The existence of a subgraph isomorphic to $F$ can be defined in first-order logic with quantifier depth no better than $\ell$, simply because no first-order formula of smaller quantifier…
The $q$-Coloring problem asks whether the vertices of a graph can be properly colored with $q$ colors. Lokshtanov et al. [SODA 2011] showed that $q$-Coloring on graphs with a feedback vertex set of size $k$ cannot be solved in time…
Previous work of the author [39] showed that the Homomorphism Preservation Theorem of classical model theory remains valid when its statement is restricted to finite structures. In this paper, we give a new proof of this result via a…
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…