One of the fundamental goals of theoretical computer science is to
understand the possibilities and limits of efficient computation. This
quest has two dimensions. The
theory of algorithms focuses on finding efficient solutions to
problems, while computational complexity theory aims to understand when
and why problems are hard to solve. These two areas have different
philosophies and use different sets of techniques. However, in recent
years there have been indications of deep and mysterious connections
In this project, we propose to explore and develop the connections between
algorithmic analysis and complexity lower bounds in a systematic way.
On the one hand, we plan to use complexity lower bound techniques as inspiration
to design new and improved algorithms for Satisfiability and other
NP-complete problems, as well as to analyze existing algorithms better.
On the other hand, we plan to strengthen implications yielding circuit
lower bounds from non-trivial algorithms for Satisfiability, and to derive
new circuit lower bounds using these stronger implications.
This project has potential for massive impact in both the areas of algorithms
and computational complexity. Improved algorithms for Satisfiability could lead
to improved SAT solvers, and the new analytical tools would lead to a better
understanding of existing heuristics. Complexity lower bound questions are
but notoriously difficult, and new lower bounds would open the way to
unconditionally secure cryptographic protocols and derandomization of
probabilistic algorithms. More broadly, this project aims to initiate greater
dialogue between the two areas, with an exchange of ideas and techniques
which leads to accelerated progress in both, as well as a deeper understanding
of the nature of efficient computation.
Call for proposal
See other projects for this call
Funding SchemeERC-CG - ERC Consolidator Grants