## New Directions in Proof Complexity

The following feature is shared by certain weak propositional proof systems: If $\psi_n$ is a uniformly generated sequence of propositional formula, and the sequence $\psi_n$ has polynomial size proofs, then the sequence $\psi_n$ in fact has polynomial size proofs that are generated in an uniform manner . For stronger propositional proof systems (like the Frege Proof Systems) this feature might fail and sporadic proofs (that are not instances of a sequence of uniform proofs) might exist. In the talk I will argue that understanding and limiting the behaviour of these sporadic proofs could be crucial for any serious progress in Propositional Proof Complexity.