2026-08-15T23:53:25Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:4372 2024-03-06T10:34:58Z ddc:004 open_access

DLOGTIME Proof Systems Krebs, Andreas Limaye, Nutan Proof systems DLOGTIME NC0 We 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 Cliquek. 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Andreas Krebs and Nutan Limaye 2013 Is Part Of LIPIcs, Volume 24, IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2013) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.FSTTCS.2013.189 urn:nbn:de:0030-drops-43725 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2013.189 eng https://creativecommons.org/licenses/by/3.0/legalcode