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Meta-complexity: A Unified Approach to the Complexity of Proofs and Computation

Project description

Tackling the deepest questions in computer science

One of the biggest mysteries in computer science is whether computational problems with quickly verifiable solutions can also be solved quickly. This is known as the P vs NP question. While most experts agree on the answer, a rigorous proof remains elusive. The ERC-funded METACOMP project aims to study this and other fundamental questions using 'meta-complexity', the theory of the complexity of problems which are themselves about complexity. By applying this theory, researchers aim to establish new lower bounds on computations and proofs, bridging proof complexity and computational complexity. METACOMP will also develop applications of this theory to cryptography, learning and approximation, offering a unified approach to some of the deepest questions in theoretical computer science.

Objective

"One of the most fundamental questions in computer science is the P vs NP question, which asks if every computational problem with efficiently verifiable solutions is efficiently solvable. Equivalently, it asks if all propositional tautologies have proofs that can be found efficiently. The answer is widely believed to be negative, but we lack a rigorous justification for this belief. The field of computational complexity approaches P vs NP and related questions by showing lower bounds (i.e. impossibility results) on efficient computations, while the field of proof complexity approaches these questions by showing lower bounds on efficient proofs for propositional tautologies. Despite much effort, the best known lower bounds in both computational complexity and proof complexity are quite far from resolving the P vs NP question, and there are significant barriers to the success of known techniques.

In this project, we will approach fundamental lower bound questions in computational complexity and proof complexity using the recently developed conceptual framework of ""meta-complexity"". Meta-complexity studies the complexity of computational problems and propositional statements that are themselves about complexity, eg., the Minimum Circuit Size Problem, which asks if a given Boolean function has small Boolean circuits. Concepts and techniques from meta-complexity have been instrumental in major recent advances in theoretical cryptography and average-case complexity, overcoming known barriers. We will extend this methodology to attack some of the deepest questions in theoretical computer science, by showing new lower bounds on both proofs and computation, establishing strong connections between computational complexity and proof complexity, and giving applications to explicit constructions, learning and hardness of approximation. A key aspect of our approach is that meta-complexity is a unifying framework, which applies equally well to proofs and computation."

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HORIZON-ERC - HORIZON ERC Grants

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Call for proposal

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(opens in new window) ERC-2024-ADG

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Host institution

THE CHANCELLOR, MASTERS AND SCHOLARS OF THE UNIVERSITY OF OXFORD
Net EU contribution

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.

€ 2 454 938,00
Address
WELLINGTON SQUARE UNIVERSITY OFFICES
OX1 2JD Oxford
United Kingdom

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Region
South East (England) Berkshire, Buckinghamshire and Oxfordshire Oxfordshire
Activity type
Higher or Secondary Education Establishments
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Total cost

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