Lower bounds for natural proof systems
Dexter C. Kozen · 1977
Two decidable logical theories are presented, one complete for deterministic polynomial time, one complete for polynomial space. Both have natural proof systems. A lower space bound of n/log(n) is shown for the proof system for the PTIME complete theory and a lower length bound of 2cn/log(n) is shown for the proof system for the PSPACE complete theory.