Related papers: Existential Second-Order Logic Over Graphs: Parame…
In this paper we address the decision problem for a fragment of set theory with restricted quantification which extends the language studied in [4] with pair related quantifiers and constructs, in view of possible applications in the field…
We study descriptive complexity of counting complexity classes in the range from #P to #$\cdot$NP. A corollary of Fagin's characterization of NP by existential second-order logic is that #P can be logically described as the class of…
One measure of the complexity of a first-order theory, and similarly a type, is the complexity of the formulas required to axiomatize it. We say a theory is bounded if there is an axiomatization involving only $\forall_n$-formulas for some…
While graphs and abstract data structures can be large and complex, practical instances are often regular or highly structured. If the instance has sufficient structure, we might hope to compress the object into a more succinct…
For every $q\in \mathbb N$ let $\textrm{FO}_q$ denote the class of sentences of first-order logic FO of quantifier rank at most $q$. If a graph property can be defined in $\textrm{FO}_q$, then it can be decided in time $O(n^q)$. Thus,…
We study first-order logic (FO) over the structure consisting of finite words over some alphabet $A$, together with the (non-contiguous) subword ordering. In terms of decidability of quantifier alternation fragments, this logic is…
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…
We analyze possibilities of second-order quantifier elimination for formulae containing parameters -- constants or functions. For this, we use a constraint resolution calculus obtained from specializing the hierarchical superposition…
We analyse the complexity of learning first-order queries in a model-theoretic framework for supervised learning introduced by (Grohe and Tur\'an, TOCS 2004). Previous research on the complexity of learning in this framework focussed on the…
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…
Solution discovery asks whether a given (infeasible) starting configuration to a problem can be transformed into a feasible solution using a limited number of transformation steps. This paper investigates meta-theorems for solution…
A strength of parameterized algorithmics is that each problem can be parameterized by an essentially inexhaustible set of parameters. Usually, the choice of the considered parameter is informed by the theoretical relations between…
We develop a well-posedness theory for second order systems in bounded domains where boundary phenomena like glancing and surface waves play an important role. Attempts have previously been made to write a second order system consisting of…
Ordered matchings, defined as graphs with linearly ordered vertices, where each vertex is connected to exactly one edge, play a crucial role in the area of ordered graphs and their homomorphisms. Therefore, we consider related problems from…
Extensional ESO is a fragment of existential second-order logic (ESO) that captures the following family of problems. Given a fixed ESO sentence $\Psi$ and an input structure $\mathbb A$ the task if to decide whether there is an extension…
Dynamic Complexity studies the maintainability of queries with logical formulas in a setting where the underlying structure or database changes over time. Most often, these formulas are from first-order logic, giving rise to the dynamic…
We study extensions of expressive decidable fragments of first-order logic with circumscription, in particular the two-variable fragment FO$^2$, its extension C$^2$ with counting quantifiers, and the guarded fragment GF. We prove that if…
The study of Description Logics have been historically mostly focused on features that can be translated to decidable fragments of first-order logic. In this paper, we leave this restriction behind and look for useful and decidable…
Over the past two decades several fragments of first-order logic have been identified and shown to have good computational and algorithmic properties, to a great extent as a result of appropriately describing the image of the standard…
The notion of bounded expansion captures uniform sparsity of graph classes and renders various algorithmic problems that are hard in general tractable. In particular, the model-checking problem for first-order logic is fixed-parameter…