Objective
The (first-order) model checking problem is a fundamental problem in theoretical computer science, bridging the fields of structural graph theory, finite model theory, and parameterized complexity.
Given as input a graph and a formula in first-order logic, the goal is to decide whether the graph satisfies the formula.
Instead of solving a single algorithmic problem, model checking algorithms provide a uniform way to solve all first-order definable problems.
Examples include parameterized versions of the dominating set, independent set, and subgraph isomorphism problems.
While model checking is hard on the class of all graphs, the recently formulated Model Checking Conjecture predicts
that a hereditary graph class admits fixed-parameter tractable first-order model checking if and only if it is monadically dependent.
Monadically dependent graph classes are very general.
They include many sparse classes like planar graphs, bounded degree, bounded tree-width, excluded minor, and nowhere dense classes; and also dense classes like monadically stable, bounded clique-width, and bounded twin-width classes.
While tractable model checking has been established for many restricted fragments of monadic dependence, the general case has so far remained elusive.
The main obstacle is the lack of a combinatorial structure theory for monadically dependent classes.
Originating in model theory, monadic dependence is defined in terms of logic and has predominantly been studied on infinite structures.
In this fellowship, I will combine tools from combinatorics and logic to develop a combinatorial structure theory for monadically dependent classes of finite graphs.
The goal is to resolve the Model Checking Conjecture and enable further progress in the algorithmic and combinatorial treatment of monadically dependent graph classes.
Fields of science (EuroSciVoc)
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: The European Science Vocabulary.
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: The European Science Vocabulary.
- natural sciences mathematics pure mathematics discrete mathematics mathematical logic
- natural sciences computer and information sciences computational science
- natural sciences mathematics pure mathematics discrete mathematics graph theory
- natural sciences mathematics pure mathematics discrete mathematics combinatorics
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Keywords
Project’s keywords as indicated by the project coordinator. Not to be confused with the EuroSciVoc taxonomy (Fields of science)
Project’s keywords as indicated by the project coordinator. Not to be confused with the EuroSciVoc taxonomy (Fields of science)
Programme(s)
Multi-annual funding programmes that define the EU’s priorities for research and innovation.
Multi-annual funding programmes that define the EU’s priorities for research and innovation.
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HORIZON.4.1 - Widening participation and spreading excellence
MAIN PROGRAMME
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Topic(s)
Calls for proposals are divided into topics. A topic defines a specific subject or area for which applicants can submit proposals. The description of a topic comprises its specific scope and the expected impact of the funded project.
Calls for proposals are divided into topics. A topic defines a specific subject or area for which applicants can submit proposals. The description of a topic comprises its specific scope and the expected impact of the funded project.
Funding Scheme
Funding scheme (or “Type of Action”) inside a programme with common features. It specifies: the scope of what is funded; the reimbursement rate; specific evaluation criteria to qualify for funding; and the use of simplified forms of costs like lump sums.
Funding scheme (or “Type of Action”) inside a programme with common features. It specifies: the scope of what is funded; the reimbursement rate; specific evaluation criteria to qualify for funding; and the use of simplified forms of costs like lump sums.
HORIZON-TMA-MSCA-PF-EF - HORIZON TMA MSCA Postdoctoral Fellowships - European Fellowships
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Call for proposal
Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
(opens in new window) HORIZON-WIDERA-2025-TALENTS-01
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Net EU financial contribution. The sum of money that the participant receives, deducted by the EU contribution to its linked third party. It considers the distribution of the EU financial contribution between direct beneficiaries of the project and other types of participants, like third-party participants.
00-927 WARSZAWA
Poland
The total costs incurred by this organisation to participate in the project, including direct and indirect costs. This amount is a subset of the overall project budget.