On p-Optimal Proof Systems and Logics for PTIME [chapter]

Yijia Chen, Jörg Flum
2010 Lecture Notes in Computer Science  
We prove that TAUT has a p-optimal proof system if and only if a logic related to least fixed-point logic captures polynomial time on all finite structures. Furthermore, we show that TAUT has no effectively p-optimal proof system if NTIME(h O(1) ) ⊆ DTIME(h O(log h) ) for every time constructible and increasing function h.
doi:10.1007/978-3-642-14162-1_27 fatcat:edzvl2e3brcrfpfui2v4vk2s3y