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DOI: 10.4230/LIPIcs.CSL.2012.440
URN: urn:nbn:de:0030-drops-36893
URL: http://drops.dagstuhl.de/opus/volltexte/2012/3689/

Kuroda, Satoru

Axiomatizing proof tree concepts in Bounded Arithmetic

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Abstract

We construct theories of Cook-Nguyen style two-sort bounded arithmetic whose provably total functions are exactly those in LOGCFL and LOGDCFL. Axiomatizations of both theories are based on the proof tree size characterizations of these classes. We also show that our theory for LOGCFL proves a certain formulation of the pumping lemma for context-free languages.

BibTeX - Entry

@InProceedings{kuroda:LIPIcs:2012:3689,
  author =	{Satoru Kuroda},
  title =	{{Axiomatizing proof tree concepts in Bounded Arithmetic}},
  booktitle =	{Computer Science Logic (CSL'12) - 26th International Workshop/21st Annual Conference of the EACSL},
  pages =	{440--454},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-42-2},
  ISSN =	{1868-8969},
  year =	{2012},
  volume =	{16},
  editor =	{Patrick C{\'e}gielski and Arnaud Durand},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2012/3689},
  URN =		{urn:nbn:de:0030-drops-36893},
  doi =		{http://dx.doi.org/10.4230/LIPIcs.CSL.2012.440},
  annote =	{Keywords: Bounded Arithmetic, LOGCFL, LOGDCFL, Proof tree}
}

Keywords: Bounded Arithmetic, LOGCFL, LOGDCFL, Proof tree
Seminar: Computer Science Logic (CSL'12) - 26th International Workshop/21st Annual Conference of the EACSL
Issue date: 2012
Date of publication: 27.08.2012


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