Project description
Advancing computational complexity theory
Complexity theory investigates lower and upper bounds on the complexity of concrete computational models. However, researchers have made very little progress in proving strong complexity lower bounds and have discovered several significant barrier results. Although a significant obstacle, these barrier results also brought to light new structural properties of complexity lower bounds connecting lower bounds to the construction of efficient learning algorithms, cryptography or independence results in mathematical logic. The EU-funded MCT project aims to continue developing these structural connections and complexity-theoretic properties of problems about complexity. It will do this by focusing on hardness magnification and structural theory. This work will provide greater insight into the central questions in computational complexity theory.
Objective
The goal of the project is to advance our understanding of the central questions in Computational Complexity Theory such as the famous P versus NP problem.
Complexity Theory approaches questions about efficiency of computation by investigating lower and upper bounds on the complexity of concrete computational models such as Boolean circuits or propositional proof systems. Unfortunately, even after several decades of intense research the progress on the question of proving strong complexity lower bounds remains very incremental. In fact, several significant barrier results have been discovered, partially explaining the complexity of establishing complexity lower bounds.
While the barrier results presented a serious obstacle they also revealed new structural properties of complexity lower bounds connecting lower bounds to the construction of efficient learning algorithms, cryptography or independence results in mathematical logic. The present project continues the development of these structural connections and complexity-theoretic properties of problems about complexity, which we shortly refer to as Metacomputational Complexity Theory.
The objectives of the project can be divided into two groups.
1. Hardness magnification, exploring limits and consequences of an emerging theory of hardness magnification which arouse recently from investigations of metacomputational aspects of circuit lower bounds and received a lot of attention as a promising approach overcoming previously existing barriers for proving complexity lower bounds.
2. Structural theory, strengthening and generalizing connections between the methods for proving lower bounds and other central concepts of computer science, such as efficient learning algorithms, cryptographic primitives and automatizability of propositional proof systems, through the lens of mathematical logic.
Fields of science
Programme(s)
Funding Scheme
MSCA-IF-EF-ST - Standard EFCoordinator
OX1 2JD Oxford
United Kingdom