ECCC-Report TR12-186https://eccc.weizmann.ac.il/report/2012/186Comments and Revisions published for TR12-186en-usSun, 30 Dec 2012 14:14:10 +0200
Paper TR12-186
| DLOGTIME-Proof Systems |
Andreas Krebs,
Nutan Limaye
https://eccc.weizmann.ac.il/report/2012/186We define DLOGTIME proof systems, DLTPS, which generalize NC0 proof systems.
It is known that functions such as Exact-k and Majority do not have NC0 proof systems. Here, we give a DLTPS for Exact-k (and therefore for Majority) and also for other natural functions such as Reach and k-Clique. Though many interesting functions have DLTPS, we show that there are languages in NP which do not have DLTPS.
We consider the closure properties of DLTPS and prove that they are closed under union and concatenation but are not closed under intersection and complement. Finally, we consider a hierarchy of polylogarithmic time proof systems and show that the hierarchy is strict. Sun, 30 Dec 2012 14:14:10 +0200https://eccc.weizmann.ac.il/report/2012/186