LIPIcs.FSTTCS.2013.189.pdf
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DLOGTIME Proof Systems
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IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2013)
Series: Leibniz International Proceedings in Informatics (LIPIcs)
Conference: IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS) - License:
Creative Commons Attribution 3.0 Unported license
- Publication Date: 2013-12-10
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Andreas Krebs and Nutan Limaye. DLOGTIME Proof Systems. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 24, pp. 189-200, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)
https://doi.org/10.4230/LIPIcs.FSTTCS.2013.189
https://doi.org/10.4230/LIPIcs.FSTTCS.2013.189
Abstract
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.
Keywords
- Proof systems
- DLOGTIME
- NC0
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