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DOI: 10.4230/LIPIcs.CSL.2015.110
Tree Grammars for the Elimination of Non-prenex Cuts

Authors: Stefan Hetzl and Sebastian Zivota

Published in: LIPIcs, Volume 41, 24th EACSL Annual Conference on Computer Science Logic (CSL 2015)

Abstract
Recently a new connection between proof theory and formal language theory was introduced. It was shown that the operation of cut elimination for proofs with prenex Pi_1-cuts in classical first-order logic corresponds to computing the language of a particular type of tree grammars. The present paper extends this connection to arbitrary (i.e. non-prenex) cuts without quantifier alternations. The key to treating non-prenex cuts lies in using a new class of tree grammars, constraint grammars, which describe the relationship of the applicability of its productions by a propositional formula.
Cite as

Stefan Hetzl and Sebastian Zivota. Tree Grammars for the Elimination of Non-prenex Cuts. In 24th EACSL Annual Conference on Computer Science Logic (CSL 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 41, pp. 110-127, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

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@InProceedings{hetzl_et_al:LIPIcs.CSL.2015.110,
  author =	{Hetzl, Stefan and Zivota, Sebastian},
  title =	{{Tree Grammars for the Elimination of Non-prenex Cuts}},
  booktitle =	{24th EACSL Annual Conference on Computer Science Logic (CSL 2015)},
  pages =	{110--127},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-90-3},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{41},
  editor =	{Kreutzer, Stephan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2015.110},
  URN =		{urn:nbn:de:0030-drops-54103},
  doi =		{10.4230/LIPIcs.CSL.2015.110},
  annote =	{Keywords: proof theory, cut-elimination, Herbrand's theorem, tree grammars}
}
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