The purpose of the project is to give a new approach, based on structural complexity techniques, to solve problems arising in field of complexity of proofs in propositional proof systems. In particular we intend to: -improve the proofs of existing lower bounds for known proof systems using new complexity techniques (like Kolmogorov Complexity);
-apply results about relationship between complexity classes to compare different proof systems;
-establish the exact correspondence between proof system complexity and circuit complexity;
-prove new lower bounds applying both new combinatorial techniques from Kolmogorov complexity and probabilistic arguments.
We intend to develop the project during the four years PhD degree requires.