Related papers: Algorithms and data structures for first-order log…
Considering systems of separations in a graph that separate every pair of a given set of vertex sets that are themselves not separated by these separations, we determine conditions under which such a separation system contains a nested…
We introduce a framework for the modeling of sequential data capturing pathways of varying lengths observed in a network. Such data are important, e.g., when studying click streams in information networks, travel patterns in transportation…
For any particular class of graphs, algorithms for computational problems restricted to the class often rely on structural properties that depend on the specific problem at hand. This begs the question if a large set of such results can be…
This paper presents a general technique for optimally transforming any dynamic data structure that operates on atomic and indivisible keys by constant-time comparisons, into a data structure that handles unbounded-length keys whose…
Sets with atoms serve as an alternative to ZFC foundations for mathematics, where some infinite, though highly symmetric sets, behave in a finitistic way. Therefore, one can try to carry over analysis of the classical algorithms from finite…
We study pseudorandomness and pseudorandom generators from the perspective of logical definability. Building on results from ordinary derandomization and finite model theory, we show that it is possible to deterministically construct, in…
We study an extension of first-order logic that allows to express cardinality conditions in a similar way as SQL's COUNT operator. The corresponding logic FOC(P) was introduced by Kuske and Schweikardt (LICS'17), who showed that query…
Separation logic and its variants can describe various properties on pointer programs. However, when it comes to properties on sequences, one may find it hard to formalize. To deal with properties on variable-length sequences and multilevel…
Separation Logic is a widely used formalism for describing dynamically allocated linked data structures, such as lists, trees, etc. The decidability status of various fragments of the logic constitutes a long standing open problem. Current…
Vector clock algorithms are basic wait-free building blocks that facilitate causal ordering of events. As wait-free algorithms, they are guaranteed to complete their operations within a finite number of steps. Stabilizing algorithms allow…
We study the problem of checking whether an existential sentence (that is, a first-order sentence in prefix form built using existential quantifiers and all Boolean connectives) is true in a finite partially ordered set (in short, a poset).…
Courcelle's Theorem states that on graphs $G$ of tree-width at most $k$ with a given tree-decomposition of size $t(G)$, graph properties $\mathcal{P}$ definable in Monadic Second Order Logic can be checked in linear time in the size of…
We study the first order theory of structures over graphs i.e. structures of the form ($\mathcal{G},\tau$) where $\mathcal{G}$ is the set of all (isomorphism types of) finite undirected graphs and $\tau$ some vocabulary. We define the…
Proving the linearizability of highly concurrent data structures, such as those using optimistic concurrency control, is a challenging task. The main difficulty is in reasoning about the view of the memory obtained by the threads, because…
This paper establishes a bridge between linear logic and mainstream graph theory, building on previous work by Retor\'e (2003). We show that the problem of correctness for MLL+Mix proof nets is equivalent to the problem of uniqueness of 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…
The celebrated notion of important separators bounds the number of small $(S,T)$-separators in a graph which are 'farthest from $S$' in a technical sense. In this paper, we introduce a generalization of this powerful algorithmic primitive…
We develop a new framework for generalizing approximation algorithms from the structural graph algorithm literature so that they apply to graphs somewhat close to that class (a scenario we expect is common when working with real-world…
One of Courcelle's celebrated results states that if C is a class of graphs of bounded tree-width, then model-checking for monadic second order logic is fixed-parameter tractable on C by linear time parameterised algorithms. An immediate…
Given a graph $G$ with source and destination vertices $s,t\in V(G)$ respectively, \textsc{Tracking Paths} asks for a minimum set of vertices $T\subseteq V(G)$, such that the sequence of vertices encountered in each simple path from $s$ to…