Objective
Computational complexity theory seeks to understand the inherent difficulty of computational problems. For example, what is the fastest algorithm for factoring? Despite decades of progress, there are still problems—such as factoring—for which we lack efficient algorithms, and yet we cannot prove that they are intrinsically hard. Still, the assumption that factoring is indeed hard underpins much of modern cryptography and e-commerce. This raises a fundamental question: Why are we unable to determine the resources required to solve many computational problems?
This project addresses such meta-complexity questions—questions about the complexity of computational problems themselves—within the field of proof complexity. While similar questions in circuit complexity have led to major breakthroughs over the past decade, their counterparts in proof complexity remain largely unexplored.
I propose a systematic study of meta-complexity problems in proof complexity, with the overarching goal of explaining why current techniques fail to prove lower bounds for many natural formulas—even in weak proof systems. I aim to map the landscape of known lower bound methods, classify them by the complexity of their proofs of correctness, and push them to their theoretical limits. I also introduce two novel meta-complexity problems: encoding-independent lower bounds and the Minimum Proof Size Problem, both of which address notable gaps in the current literature.
By pursuing these goals, I seek to identify fundamental barriers and to guide future research in the field. Moreover, just as the study of the Minimum Circuit Size Problem has revealed deep connections to cryptography, learning theory, and derandomisation, a systematic investigation of analogous questions in proof complexity may uncover similar links to other areas. Ultimately, this project contributes to the broader aim of understanding the limits of efficient computation and efficient reasoning.
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 computer and information sciences computer security cryptography
- social sciences economics and business business and management commerce e-commerce
You need to log in or register to use this function
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.
-
HORIZON.1.1 - European Research Council (ERC)
MAIN PROGRAMME
See all projects funded under this programme
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-ERC - HORIZON ERC Grants
See all projects funded under this funding scheme
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) ERC-2026-STG
See all projects funded under this callHost institution
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.
22100 Lund
Sweden
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.