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Researcher profile

Victor Lagerkvist

Victor Lagerkvist contributes to research discovery and scholarly infrastructure.

ResearcherAffiliation not importedOpen to collaborate
Computational ComplexityArtificial IntelligenceLogic in Computer Science

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Published work

4 published item(s)

preprint2026arXiv

Clausal Deletion Backdoors for QBF: a Parameterized Complexity Approach

Determining the validity of a quantified Boolean formula (QBF) is a PSPACE-complete problem with rich expressive power. Despite interest in efficient solvers, there is, compared to problems in NP, a lack of positive theoretical results, and in the parameterized complexity setting one often has to restrict the quantifier prefix (e.g., bounding alternations) to obtain fixed parameter tractability (FPT). We propose a new parameter: the number of variables in clauses that has to be removed before reaching a tractable class (a clause covering (CC) backdoor). We are then interested in solving QBF in FPT time given a CC-backdoor of size $k$. We consider the three classical, tractable cases of QBF as base classes: Horn, 2-CNF, and linear equations. We establish W[1]-hardness for Horn but prove FPT for the others, and prove that in a precise, algebraic sense, we are only missing one important case for a full dichotomy. Our algorithms are non-trivial and depend on propagation, and Gaussian elimination, respectively, and are comparably unexplored for QBF.

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preprint2025arXiv

Complexity of Faceted Explanations in Propositional Abduction

Abductive reasoning is a popular non-monotonic paradigm that aims to explain observed symptoms and manifestations. It has many applications, such as diagnosis and planning in artificial intelligence and database updates. In propositional abduction, we focus on specifying knowledge by a propositional formula. The computational complexity of tasks in propositional abduction has been systematically characterized - even with detailed classifications for Boolean fragments. Unsurprisingly, the most insightful reasoning problems (counting and enumeration) are computationally highly challenging. Therefore, we consider reasoning between decisions and counting, allowing us to understand explanations better while maintaining favorable complexity. We introduce facets to propositional abductions, which are literals that occur in some explanation (relevant) but not all explanations (dispensable). Reasoning with facets provides a more fine-grained understanding of variability in explanations (heterogeneous). In addition, we consider the distance between two explanations, enabling a better understanding of heterogeneity/homogeneity. We comprehensively analyze facets of propositional abduction in various settings, including an almost complete characterization in Post's framework.

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preprint2022arXiv

Component twin-width as a parameter for BINARY-CSP and its semiring generalisations

We investigate the fine-grained and the parameterized complexity of several generalizations of binary constraint satisfaction problems (BINARY-CSPs), that subsume variants of graph colouring problems. Our starting point is the observation that several algorithmic approaches that resulted in complexity upper bounds for these problems, share a common structure. We thus explore an algebraic approach relying on semirings that unifies different generalizations of BINARY-CSPs (such as the counting, the list, and the weighted versions), and that facilitates a general algorithmic approach to efficiently solving them. The latter is inspired by the (component) twin-width parameter introduced by Bonnet et al., which we generalize via edge-labelled graphs in order to formulate it to arbitrary binary constraints. We consider input instances with bounded component twin-width, as well as constraint templates of bounded component twin-width, and obtain an FPT algorithm as well as an improved, exponential-time algorithm, for broad classes of binary constraints. We illustrate the advantages of this framework by instantiating our general algorithmic approach on several classes of problems (e.g., the $H$-coloring problem and its variants), and showing that it improves the best complexity upper bounds in the literature for several well-known problems.

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preprint2013arXiv

Weak Bases of Boolean Co-Clones

Universal algebra and clone theory have proven to be a useful tool in the study of constraint satisfaction problems since the complexity, up to logspace reductions, is determined by the set of polymorphisms of the constraint language. For classifications where primitive positive definitions are unsuitable, such as size-preserving reductions, weaker closure operations may be necessary. In this article we consider strong partial clones which can be seen as a more fine-grained framework than Post's lattice where each clone splits into an interval of strong partial clones. We investigate these intervals and give simple relational descriptions, weak bases, of the largest elements. The weak bases have a highly regular form and are in many cases easily relatable to the smallest members in the intervals, which suggests that the lattice of strong partial clones is considerably simpler than the full lattice of partial clones.

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