Objective
One of the most fundamental and notorious open problems in theoretical computer science is the possible existence of highly efficient algorithms solving NP problems: there might be fast algorithms breaking established cryptosystems, automating theorem proving, making contemporary approaches to AI obsolete, and solving practically every computational task. This issue lies at the heart of the P versus NP problem, a central question of computational complexity, and particularly in the investigation of lower bounds on the efficiency of concrete computational models such as Boolean circuits.
The notorious difficulty of proving complexity lower bounds became evident already in the early days of the theory of computing when the theory of formal barriers explaining their difficulty started to emerge. In recent years, there has been a dramatic rise of barrier results driving the field forward and connecting it to areas such as learning theory and cryptography. A better understanding of formal barriers is emerging today as the necessary requirement for further progress on central problems in computational complexity, and the goal of this project is to develop a systematic theory around it: proof complexity of circuit lower bounds. In particular, the project will bridge the rich tradition of concrete combinatorial methods with the new meta-mathematical approach via the phenomena of hardness magnification that connect strong and weak computational models. It will focus on a logic-oriented area of proof complexity investigating the lengths of propositional proofs and use its meta-mathematical perspective to explore the potential of lower bound methods in circuit complexity but also in proof complexity itself.
The proposed meta-mathematical approach presents a novel perspective on established topics in computational complexity with a potential to deliver a paradigmatic shift in the field and bring us closer to the full understanding of the power of computing.
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.
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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.1.1 - European Research Council (ERC)
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-ERC - HORIZON ERC Grants
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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) ERC-2025-COG
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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.
OX1 2JD Oxford
United Kingdom
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.