Related papers: Fixed-parameter tractability, definability, and mo…
We prove a general decomposition theorem for the modal $\mu$-calculus $L_\mu$ in the spirit of Feferman and Vaught's theorem for disjoint unions. In particular, we show that if a structure (i.e., transition system) is composed of two…
A conjecture in algorithmic model theory predicts that the model-checking problem for first-order logic is fixed-parameter tractable on a hereditary graph class if and only if the class is monadically dependent. Originating in model theory,…
Formalisms based on temporal logics interpreted over finite strict linear orders, known in the literature as finite traces, have been used for temporal specification in automated planning, process modelling, (runtime) verification and…
In parametric lock-sharing systems processes can spawn new processes to run in parallel, and can create new locks. The behavior of every process is given by a pushdown automaton. We consider infinite behaviors of such systems under strong…
When modeling an application of practical relevance as an instance of a combinatorial problem X, we are often interested not merely in finding one optimal solution for that instance, but in finding a sufficiently diverse collection of good…
Logics with team semantics provide alternative means for logical characterization of complexity classes. Both dependence and independence logic are known to capture non-deterministic polynomial time, and the frontiers of tractability in…
The complexity class $NP$ can be logically characterized both through existential second order logic $SO\exists$, as proven by Fagin, and through simulating a Turing machine via the satisfiability problem of propositional logic SAT, as…
In this contribution we revisit regular model checking, a powerful framework that has been successfully applied for the verification of infinite-state systems, especially parameterized systems (concurrent systems with an arbitrary number of…
Since its development in the early 90's, parameterized complexity has been widely used to analyze the tractability of many NP-hard combinatorial optimization problems with respect to various types of problem parameters. While the generic…
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 (MSO_2) is fixed-parameter tractable (fpt) on C by linear time parameterized algorithms,…
We give a new, direct proof of the tetrachotomy classification for the model-checking problem of positive equality-free logic parameterised by the model. The four complexity classes are Logspace, NP-complete, co-NP-complete and…
Continuous first-order logic is used to apply model-theoretic analysis to analytic structures (e.g. Hilbert spaces, Banach spaces, probability spaces, etc.). Classical computable model theory is used to examine the algorithmic structure of…
We construct a fixed parameter algorithm parameterized by d and k that takes as an input a graph G' obtained from a d-degenerate graph G by complementing on at most k arbitrary subsets of the vertex set of G and outputs a graph H such that…
Several works have recently investigated the parameterized complexity of data completion problems, motivated by their applications in machine learning, and clustering in particular. Interestingly, these problems can be equivalently…
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 show that for various classes C of sparse graphs, and several measures of distance to such classes (such as edit distance and elimination distance), the problem of determining the distance of a given graph G to C is fixed-parameter…
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…
We consider two matrix completion problems, in which we are given a matrix with missing entries and the task is to complete the matrix in a way that (1) minimizes the rank, or (2) minimizes the number of distinct rows. We study the…
We present an almost complete classification of the parameterized complexity of all operator fragments of the satisfiability problem in computation tree logic CTL. The investigated parameterization is the sum of temporal depth and…
The basic (and traditional) crossing number problem is to determine the minimum number of crossings in a topological drawing of an input graph in the plane. We develop a unified framework yielding fixed-parameter tractable (FPT) algorithms…